ownership

Markets for Ownership


by


Joshua S. Gans
*

Melbourne Business School
University of Melbourne

First Draft: 18
th
September, 1999
This Version: 20 February 2001




The prevailing economic theory of the firm, based on a property rights
perspective, has demonstrated that ownership by dispensable, outside parties is
an inefficient outcome relative to ownership by productive agents. In order to
better understand observed patterns of ownership, this paper considers the
outcome of markets for ownership that operate prior to production taking place.
The main result is that outside parties will often become the equilibrium asset
owners. This is precisely because, but for ownership, such parties would not earn
rents. In contrast, productive agents earn rents even when they do not own assets.
Given that their contribution is complementary with other productive agents,
their willingness-to-pay for ownership is less than that of an outside party. This
result is robust to the introduction of moderate levels of inefficiency arising from
outside ownership and to a consideration of opportunities for re-sale before
production begins. The main conclusion drawn is that the nature of the operation
of markets for ownership stands alongside incentive effects as important
predictors of firm boundaries. Journal of Economic Literature Classification
Numbers: D23, L22

Keywords. ownership, property rights, outside parties, firm boundaries, Coase,
incomplete contracts, equilibrium, resale.



*
Thanks to Susan Athey, Catherine de Fontenay, Patrick Francois, Oliver Hart, Bengt Holmstrom, Rohan
Pitchford, Eric Rasmusen, Rabee Tourky, seminar participants at the University of Melbourne, University
of New South Wales and Harvard University, and, especially, Stephen King and Scott Stern for helpful
discussions. Responsibility for all views expressed lies with the author. All correspondence to Joshua Gans:
[email protected]. The latest version of this paper is available at: www.mbs.unimelb.edu.au/jgans.

It is now commonplace to define a firm with regard to the ownership of a
collection of assets (Hart, 1995). Under this definition, a firm does not extend beyond the
assets its owners control. However, when all relevant variables that impact on those
assets’ value can be readily contracted upon, Coasian logic suggests that the efficient
assignment of assets to controlling agents is indeterminate. That is, any ownership
structure will lead to the same level of value created. So, if it is presumed that the
allocation of ownership in the economy is efficient, under complete contracting, any such
allocation could occur.
The lack of predictive power of this property rights view of the firm has led to a
focus on the limits to contractibility and the consequences flowing from the non-
contractibility of key decisions. This incomplete contracts literature is exemplified by the
approach of Grossman and Hart (1986) and Hart and Moore (1990); hereafter GHM. The
main contribution of GHM is the provision of a precise framework for exploring the
relationship between asset ownership and incentives to undertake non-contractible
actions. The basic logic is simple: while ownership does not matter for efficiency ex post,
it does matter for distribution. In particular, owners of assets command superior
bargaining power afforded by their ability to exclude others from profiting or using their
assets. That bargaining power assures them a greater share of ex post surplus from the
asset and hence, directs them to take non-contractible actions ex ante that maximise that
surplus. Consequently, different ownership structures will have an impact on overall
efficiency.
GHM use this framework to generate a host of insights into what type of
ownership structures will be efficient. This includes findings that important and
2
indispensable agents should own assets, while dispensable, outside parties should not.
They also demonstrate that joint ownership – in the sense that more than one agent has
veto power over an asset’s use – is less efficient than other structures. Basically, joint
veto rights as well as structures that assign sole ownership of assets to dispensable agents
serve merely to reduce surplus to those ‘productive’ agents who can undertake non-
contractible actions and as a consequence, ownership changes that assign control rights to
those productive agents can be efficiency enhancing.
The inefficiency of outside party and joint ownership raise a host of empirical
puzzles as such structures are commonly observed. Individual shareholders and mutual
funds, which rarely take important actions, own firms. Moreover, much ownership is
concentrated in the hands of a few individuals who are neither indispensable for value
creation nor take important, but non-contractible, actions (Holmstrom and Roberts,
1998).
In this paper, I suggest that an explanation for these observations lies in the nature
of ex ante markets for asset ownership. To explore this, I utilise the GHM model of
behaviour, bargaining and surplus generation following the allocation of ownership but
model that allocation is arising from the outcome of non-cooperative interactions
between agents. This stands in contrast to the cooperative approach employed by GHM
that allows the coalition of all agents to allocate ownership efficiently.
1
Not surprisingly,
a non-cooperative approach may give rise to inefficient allocations, however, my main
goal is to explore how the introduction of a market for ownership can generate more

1
See Hart (1995, p.43) for a statement. The basic assumption there is that all agents can effect ex ante
transfers and implement an efficient structure. In contrast, here it will be assumed that such ex ante
transfers are limited to bilateral ones between agents.
3
precise predictions regarding firm boundaries when those boundaries are defined by the
extent of asset ownership.
2

There are two key conclusions that result from the introduction of a market for
ownership. First, while dispensability is a key criterion for ruling out ownership under
GHM, it becomes an important predictor of ownership patterns when assets are allocated
in a market. This is precisely because when they do not own assets, dispensable agents
are unable to earn rents making them intense competitors for asset ownership. Second, a
market for ownership enables predictions regarding ownership structures and rent
distribution even in those settings where all investments are contractible and there is no
linkage between ownership and incentives. Indeed, while ownership continues not to
matter for efficiency, in a contractible world, this paper also highlights that efficiency is
not the only criterion that should be employed to understand real patterns of asset
ownership. Specifically, for a variety of theoretical and policy concerns, there is interest
in the identity of asset owners, independent of their incentive effects. This paper suggests
that the mechanism by which asset ownership is determined will have an impact on both
patterns of asset ownership as well as efficiency.
To illustrate these key conclusions it is useful to consider a simple example.
Suppose that a buyer wishes to purchase a good from a specific seller. The buyer is the
seller’s only potential customer although the buyer can purchase an inferior good
elsewhere leaving them with value of $30 in that instance. Production of both goods
requires the use of a particular asset. In addition, the value of the good to the buyer

2
Bolton and Whinston (1993) also considered non-cooperative processes for the allocation of asset
ownership. Their approach, while related to the one pursued here, is distinct in that it did not consider the
key role the outside parties play in such environments. I will comment more on the relationship between
their results and the results in this paper below.
4
depends upon the seller making a specific investment (say, that lowers supply costs).
With the investment, total value created is $100; otherwise it i s $80. The investment costs
the seller $10; so it is socially worthwhile. In this situation, if the seller owns the asset, if
the investment is contractible, the buyer and seller split $90 while, if the buyer owns the
asset, using their additional source as a threat means they receive $60 while the seller
receives $30.
It is also possible that an outside party could own the asset. In this situation, the
seller, buyer and outside party receive $20, $35 and $35 (using the Shapley value
3
).
Notice that the value of ownership is $35 for an outside party as they would otherwise
receive nothing. On the other hand, for the seller and buyer, the value of ownership is
assessed relative to what they would receive if they did not own. Thus, the seller places a
value of (at most) $25 (= $45 - $20) while the buyer also places a value of (at most) $25
(= $60 - $35) on ownership. Each of these is less than the outside party’s value and
hence, if each were to individually bid for ownership in an open auction, the outside party
would own the asset.
This prediction is the central insight of this paper. It is not specific to this example
and arises naturally in the commonly assumed environment that underlies the GHM
approach. It is also robust to several extensions. For instance, for a modest degree of
inefficiency arising from outside ownership when investments are non-contractible, it is
easy to demonstrate that the outside party still values ownership above those of the buyer

3
This bargaining outcome is commonly used in the GHM approach and it will be employed throughout this
paper. There are two reasons for this. First, many of results of GHM and here are robust to alternative
bargaining rules (Hart and Moore, 1990). Second, in the setting of this paper there will be a single asset
essential to all agents. In this environment, there is a persuasive non-cooperative foundation for the Shapley
value (Stole and Zwiebel, 1996a).
5
and seller.
4
This is a general result that so long as the efficiency-enhancing incentives
from ownership are not too great, outside ownership is the unique equilibrium outcome of
an initial auction.
In addition, this result is robust to the possibility that asset owners may re-sell the
asset to other agents. Section 3 develops a model of re-sale demonstrating that outside
owners will choose to produce rather than re-sell assets so long as resale opportunities do
not arrive too frequently. If that occurs it is possible that the outside owner may prefer to
play productive agents off against each other; with each valuing the profits from resale
that arise principally at the expense of other productive agents.
5
Nonetheless, even if
resale opportunities arise frequently, productive agents will always have an incentive to
re-sell assets rather than produce; thereby increasing the likelihood that an inefficient
ownership allocation will ultimately result.
The potential explanation for outside ownership provided here is complementary
to other explanations that have been developed in the literature. This includes models
demonstrating that when non-contractible investments impact negatively on agents’
outside options, ownership may reduce incentives for agents to take productive actions
(de Meza and Lockwood, 1998; Rajan and Zingales, 1998; Chiu, 1998; and Baker,
Gibbons and Murphy, 2000) and also the consequences of wealth constraints on
productive agents that make it difficult for them to purchase assets ex ante (Aghion and
Tirole, 1994). Finally, Holmstrom (1999) argues that other incentive instruments that can

4
The seller receives $40 (= $50 - $10) if it owns the asset; the same amount as if it does not invest. Under
buyer-ownership the seller does not invest as they would receive $25 rather than $30 by not investing.
Similarly, under outside-ownership the seller would only receive $40/3 by investing as opposed to $50/3
otherwise. Thus, the seller’s willingness-to-pay for ownership is $70/3 as opposed to $55/3 for the buyer
and $95/3 for the outside party.
5
Therefore, the outside party can exploit potential negative externalities that arise from resale opportunities
in a similar manner to situations examined by Segal (1999).
6
substitute for ownership and these have proven quite effective for, say, employees of
firms. Here the role of the firm is considered to be one of coordinating these various
incentive instruments and, as a consequence, outside parties may be the appropriate
owners of a firm’s assets.
6
Each of these research streams could be integrated into the
framework developed here for analysing ex ante asset ownership so as to develop a richer
set of empirical predictions regarding firm boundaries.
The general prediction here, that markets for ownership can drive outside party
ownership, ultimately rests upon the assumed non-cooperative structure of ex ante asset
allocation. Indeed, when there are relatively few productive agents who may work with
an asset, it seems plausible that a cooperative asset allocation mechanism may operate. In
particular, as is demonstrated in Section 4, in such cases, productive agents may be able –
through cooperative bidding in asset markets – secure joint ownership of an asset and
perhaps, depending upon internal contracting difficulties, restructure arrangements so that
outcomes are efficient.
The market forces identified here are likely to be important when it is difficult for
productive agents to form coalitions in asset markets that will allow for a cooperative
outcome. Essentially, the same conditions that make the efficient private provision of
public goods difficult are the same types of conditions that will lead to outside ownership
structures being observed. In particular, as is addressed in Section 4, such difficulties will
arise when there are relatively large numbers of productive agents and it is difficult to
identify clearly important agents among them. This accords with observations of outside
party ownership among large corporations, newly privatised firms in transition
economies and venture capital equity in entrepreneurial start-ups; each of which

6
See also Holmstrom and Milgrom (1994) and Holmstrom and Roberts (1998).
7
potentially result from issues of coordinating asset market behaviour by a large number
of productive agents. These applications are discussed in more detail in Section 5. A final
section concludes and offers directions for future research.
1. Initial Set-Up
Suppose there are two productive agents (A and B) and potentially many outside
parties (of type O). Outside parties are perfectly substitutable in a productive sense. There
is a single alienable asset that is owned (initially at least) by another agent for whom the
value of the asset is normalised to zero.
A and B can each make asset-specific investments (or take other actions) that can
generate value so long as A, B or both can work in association with the asset. A and B’s
investments are privately costly – incurring a and b, respectively – but give rise to total
value created of ( , ) v a b if each works with the asset; where v is assumed to be non-
decreasing in both its arguments. If, however, only one agent is associated with the asset,
that agent allows value of ( ) ( ,0)
A
v a v a ≡ and ( ) (0, )
B
v b v b ≡ (depending on the agent
concerned) while the other agent generates no additional value. In this sense, the asset
itself is necessary for any value to be created and so is essential
7
to all agents.
Note, also, that – at least in the first best world – it assumed that it is desirable for
both A and B to work with the asset. That is, let
,
max ( , )
a b
V v a b a b · − − ,
max ( )
A a A
V v a a · − and max ( )
B b B
V v b b · − so that max{ , }
A B
V V V ≥ . Finally, as in

7
According to the definition of Hart and Moore (1990).
8
much of the incomplete contracts literature, it is assumed that a and b are complements in
generating ( , ) v a b ; that is, ( , ) v a b is supermodular in a and b.
8

On the other hand, an O’s association with the asset has no influence the value of
production from any coalition controlling the asset. Thus, following the definitions of
Hart and Moore (1990), O is a dispensable, outside party.
The timing of the model is as follows:
DATE 0: The initial owner of the asset auctions ownership of the asset; with each
agent submitting a bid and the owner choosing the highest bid.
9

DATE 1: A and B choose their investments, a and b.
DATE 2: All agents negotiate over the division of ( , ) v a b where the precise
division is based on the Shapley value.
10
Production takes place and
payments are made.
This is precisely the same model timing that arises in GHM where a and b are considered
non-contractible. The only difference from that literature is the allocation mechanism of
date 0. As noted earlier, GHM assume that all agents can negotiate (with transfers) over
the date 0 allocation of asset ownership. In contrast, this paper assumes that the allocation
mechanism is market-based, in this case an auction.
As will be demonstrated below, constraints upon how agents can bid for and
transfer ownership between each other will play an important role in the final
equilibrium. Initially, it is assumed that agents must participate in auctions as individuals
and are not able to collude or cooperate. This assumption rules out forms of joint
ownership and also distinguishes the market-based allocation mechanisms considered
here from the cooperative mechanisms considered by GHM. It is also, initially, assumed

8
These assumptions are equivalent to Hart and Moore’s (1990) assumptions 5 and 6.
9
Given complete information, the form of the auction is unimportant.
10
In this case, because the asset is essential, the Shapley value can be derived from a non-cooperative
9
that the initial auction allocates ownership without any further opportunities for re-sale.
In later sections, however, this assumption is relaxed and re-sales by further (potentially
discriminatory) auctions are permitted at any time up until date 1.
2. Market Allocations of Ownership
A standard result in GHM is that ownership should not be allocated to outside
parties (such as agent O in this model). There are qualifiers to this standard result. For
instance, productive agents may be subject to wealth constraints that may prevent the
efficient ownership allocation from arising in ex ante negotiations.
11
Alternatively, some
ownership structures that allocate ownership to a particular productive agent have less
balanced incentives than ownership structures involving an outside party. However, the
strong prediction remains that the outside party should not be given sole ownership of an
asset that is essential to another productive agent.
12

This section demonstrates that, under the model of Section 1, the unique
equilibrium outcome often involves O owning the asset. This is always the case when
agents’ investments are contractible but also when outside ownership leads to a moderate
degree of reduced incentives relative to productive agent ownership.

bargaining game where date 1 prices are non-binding until production begins (see Stole and Zwiebel,
1996a, 1996b).
11
See Aghion and Tirole (1994).
12
See Hart and Moore (1990, footnote 20). Their Corollary (p.1137) states that outside parties should not
receive any control rights if stochastic control is possible. However, their Proposition 11 has a stronger
implication that even where stochastic control is not possible, an outside party should not be the sole owner
of an essential asset.
10
Equilibrium Under Complete Contracting
It is useful to begin by considering the case of complete contracting. In this case,
the date 1 actions of A and B can be negotiated and surplus can be allocated accordingly.
In effect, dates 1 and 2 are combined. This means that the ownership structure does not
matter for efficiency in that total value is maximised in any agreement and that the agent
that owns the asset appropriates the largest share of V. The resulting payoffs (in date 1-2)
to each agent are summarised in Table 1.

Table 1: Negotiated Payoffs Under Complete Contracting

Payoffs Ownership
Structure A B O
A-Ownership
1
2
( )
A
V V +
1
2
( )
A
V V − 0
B-Ownership
1
2
( )
B
V V −
1
2
( )
B
V V + 0
O-Ownership ( )
1 1
3 2 B A
V V V − + ( )
1 1
3 2 A B
V V V − + ( )
1 1
3 2
( )
A B
V V V + +


With this set-up, one can prove the following proposition (whose proof is in the
appendix).
Proposition 1. The unique equilibrium outcome is ownership by O.

The intuition behind the proposition is relatively straightforward. Note, first, that O only
receives a positive payoff when it owns the asset. The ‘productive’ agents, A and B,
receive positive payoffs regardless of who owns the asset. However, the complementarity
between A and B means that a productive agent’s payoff is higher when the other
productive agent owns the asset compared with what they receive under O-ownership.
This means that they are effectively competing with O when bidding for the asset;
however, their willingness-to-pay for ownership is the difference between their payoff
11
when they own the asset and their payoff under O-ownership. Because of their
complementarity, O cannot easily play each productive agent off against the other,
making their payoff under O-ownership relatively high. Ultimately, this means that the
willingness-to-pay of A or B will be less than that of O; making O-ownership the unique
equilibrium.
Note that the assumed complementarity here – implying that, say, B’s payoff
under A-ownership exceeds its payoff under O-ownership – is the critical condition in the
proof as it implies that
A B
V V V > + .
13
Any bargaining outcome that leads to this ranking
will result in O-ownership being the unique equilibrium outcome. In particular, most
solutions to random-order bargaining games – of which the Shapley value is an example
– will generate this ranking (see Segal, 2000). Consequently, the results here would hold
for many cooperative bargaining models beyond the Shapley outcome commonly used in
this literature.
14

A current viewpoint held by researchers on the theory of the firm is that, in an
environment where all relevant variables are contractible, economic theory does not
provide any predictions as to the size of firms and firm boundaries. Coasian logic tells us
that all ownership patterns yield the same level of efficiency and, consequently, one
cannot predict firm boundaries using an efficiency criterion alone (Hart, 1995).

13
If A and B were substitutes, then
A B
V V V < + and either A or B ownership could be an equilibrium
outcome. This is because, under O-ownership, O is able to play A and B against one another reducing their
payoff under that regime. If
A B
V V V · + , then any agent could end up owning the asset in equilibrium.
14
In the model here, the asset owner is indispensable. Hence, when there is O-ownership, collusion
between A and B would assist O as neither A or B could negotiate over their marginal contributions that
exceed their average contribution under complementary. This means that, under O-ownership, A and B’s
payoffs are sufficiently high, reducing their individual willingnesses-to-pay for ownership. Segal (2000)
demonstrates that this property is common to most random-order bargaining games. This property would
als o hold for the bargaining model employed by Brandenburger and Stuart (2000) that is based on the core.
12
Nonetheless, Proposition 1 demonstrates that, even when ownership does not
matter for efficiency, this does not imply that one cannot use economic theory to generate
predictions regarding firm boundaries. The private value of ownership differs among
agents with outside parties placing the greatest value on ownership, as this is the only
situation they earn any rents. Thus, there is a strong equilibrium tendency towards
ownership by outside parties; providing a potential explanation for observed patterns of
firm ownership.
Proposition 1 does rely, however, on A and B being unable to collude at date o
and submit bids for joint ownership of the asset. If joint ownership (defined as allowing
all owners to have veto rights over control of the asset) is possible, then either it or O-
ownership is an equilibrium outcome. To see this, note that under joint ownership by A
and B, each earns
1
2
V . If they bid together for ownership, A and B would be willing-to-
pay ( )
1 1
3 2
2 ( )
A B
V V V V − − + which is precisely equal to O’s willingness-to-pay.
15
So,
regardless of the precise relationship between total surplus and outside options, joint
ownership or O-ownership will be the equilibrium outcome.
In summary, the complete contracting case is a useful benchmark in identifying
biases in the private value of ownership that impact the equilibrium (as opposed to
efficient) allocation of property rights. As is demonstrated next, this bias is inherent in all
models of asset ownership even as contracts become incomplete.

15
If A and B can submit individual bids in addition to their joint bid, each will bid at most
1 1 1
2 2 2
( )
i i
V V V V + − · for i = A or B. Each is necessarily less than O’s bid.
13
Equilibrium Under Incomplete Contracting
Suppose now that the investments, a and b, are not contractible (with dates 1 and
2 distinct). Once again, using the Shapley value, the date 2 division of the surplus under
each ownership structure is as follows:

Table 2: Negotiated Date 2 Payoffs Under Incomplete Contracting

Payoffs Ownership
Structure A B O
A-Ownership
1
2
( ( , ) ( ))
A
v a b v a +
1
2
( ( , ) ( ))
A
v a b v a −
0
B-Ownership
1
2
( ( , ) ( ))
B
v a b v b −
1
2
( ( , ) ( ))
B
v a b v b +
0
O-Ownership ( )
1 1
3 2
( , ) ( ) ( )
B A
v a b v b v a − + ( )
1 1
3 2
( , ) ( ) ( )
A B
v a b v a v b − +
( ) ( )
1 1
3 2
( , ) ( ) ( )
A B
v a b v a v b + +


At date 1, knowing the ownership structure, both A and B will choose their respective
investments to maximise their ex post payoffs. Let ˆ( ) v i , ˆ ( )
A
v i and ˆ ( )
B
v i be the realised
total surplus and outside options taking into account the privately optimal choices of a
and b (denoted ˆ( ) a i and
ˆ
( ) b i ), respectively, given an ownership structure
{ ¦ -ownership, -ownership, -ownership i A B O ∈ . Then the ex post payoffs for each agent,
given each ownership structure are summarised in Table 3.

Table 3: Expected Payoffs Under Incomplete Contracting

Payoffs Ownership
Structure A B O
A-
Ownership
1
2
ˆ ˆ ˆ ( ( ) ( )) ( )
A
v A v A a A + −
1
2
ˆ
ˆ ˆ ( ( ) ( )) ( )
A
v A v A b A − − 0
B-
Ownership
1
2
ˆ ˆ ˆ ( ( ) ( )) ( )
B
v B v B a B − −
1
2
ˆ
ˆ ˆ ( ( ) ( )) ( )
B
v B v B b B + − 0
O-
Ownership
( )
1 1
3 2
ˆ ˆ ˆ ˆ ( ) ( ) ( ) ( )
B A
v O v O v O a O − + − ( )
1 1
3 2
ˆ
ˆ ˆ ˆ ( ) ( ) ( ) ( )
A B
v O v O v O b O − + − ( )
1 1
3 2
ˆ ˆ ˆ ( ) ( ( ) ( ))
A B
v O v O v O + +


14
As suggested by the complete contracting case, it is possible to find conditions
under which O-ownership is the unique equilibrium outcome.
Proposition 2. O-ownership is the unique equilibrium outcome if

( ) { ¦
1
{ , } 3
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ( ) ( ) ( ) max ( ) ( ) ( ) ( )
A B i A B i i
v O v O v O v i v i v O v O
∈
− − > + − −
The proof of this proposition is in the appendix. This condition is sufficient to ensure that
O’s willingness-to-pay for the asset exceeds that of both A and B. Essentially, the
condition requires that the incentive benefits from ownership are not too high. However,
it also requires that, even under O-ownership, the investments of A and B are sufficiently
complementary. In this were not the case, then A and B would appropriate fewer rents
under O-ownership and be willing to pay more for ownership themselves.
A strengthening of the condition of Proposition 2 yields a necessary and sufficient
condition for O-ownership.
Corollary 1. The unique equilibrium outcome is O-ownership if and only if:
(i) ( )
1 1 1
2 3 2
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ( ) ( ) ( ( ) ( )) 2 ( ) ( ) ( )
A B A
a A a O v A v A v O v O v O − > + − − + and
(ii) ( )
1 1 1
2 3 2
ˆ ˆ
ˆ ˆ ˆ ˆ ˆ ( ) ( ) ( ( ) ( )) 2 ( ) ( ) ( )
B A B
b B b O v B v B v O v O v O − > + − − + .
Moreover, there exists 0 ε > such that if { ¦
ˆ ˆ ˆ max ( ), ( ) ( ) v A v B v O ε − < , (i) and (ii) are
satisfied.

Once again the proof is in the appendix. This corollary demonstrates that the result in
Proposition 1 continues to hold so long as non-contractible investments are of moderate
importance.
To see the possibility of O-ownership more clearly, suppose that A and B’s
contributions are so highly complementary that each is indispensable (that is, their
outside options are zero). For this case that the GHM framework offered a clear
15
prediction: that either A or B should own the asset.
16
Then a sufficient condition for O-
ownership to be the unique equilibrium is that:

{ ¦
ˆ ˆ ˆ max ( ), ( ) ( )
1
ˆ( ) 3
v A v B v O
v O
−
< .
17

That is, when the efficiency effect of ownership on total surplus is less than a 33.33
percent improvement, O will have the highest willingness-to-pay for the asset.
Example: Suppose that only A has an investment choice. That choice is discrete –
{0,1} a ∈ – with cost of 100a. Suppose that (1) 300 v · and (0) 180 v · if both A and B
work with the asset, whereas (1) 100
A
v · , (0) 50
A
v · and (1) (0) 100
B B
v v · · . In this
case, a choice of a = 1 is socially efficient; however, it will only be take under A-
ownership. The various payoffs under each ownership structure are, therefore:

Payoffs Ownership
Structure A B O
A-Ownership 100 100 0
B-Ownership 40 140 0
O-Ownership 35 60 85

Note that the conditions of Proposition 2 are satisfied as 100 – 35 = 65 < 85 and 140 –
60 = 80 < 85. Hence, O-ownership is the unique equilibrium.

As in the previous section, it is important to emphasise that this result hinges on
the absence of collusion between A and B in the date 0 market allocation process. If joint
ownership by A and B (which is denoted by J) is possible, where both agents can veto the
asset’s use, then a joint bid for such ownership will out-bid O-ownership if,
ˆ ˆ
ˆ ˆ ˆ ˆ ( ) ( ) ( ) ( ) ( ) ( ) v J v O a J a O b J b O − ≥ − + − ; if it creates greater surplus. However, joint
ownership will only be an equilibrium if individual bids for ownership are less than the
value created under joint ownership. This will be the case if

16
See Hart and Moore (1990, Proposition 6).
17
Actually, in this case, ˆ ˆ ( ) ( ) v A v B · because ownership does not actually change either agent’s bargaining
position. See Maskin and Tirole (1999). In the appendix, the general case of N productive agents is
considered. There it is demonstrated that as the number of productive agents becomes larger, the condition
for O-ownership to be the unique equilibrium falls. That is, so long as the growth in surplus (from
16
( ) ( )
3 1 1
2 2 2
ˆ ˆ ˆ
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ max ( ( ) ( )) ( ) ( ) , ( ( ) ( )) ( ) ( ) ( ) ( ) ( )
A B
v A v A a A a J v B v B b B b J v J a J b J + − − + − − < − − ]
]

Thus, joint ownership will be the unique equilibrium outcome so long as the incentive
effects arising from joint over individual ownership are not too great.
18
Note, however,
that in the GHM framework both O and J-ownership are inefficient in the environments
assumed here. Each results in lower surplus than under A or B-ownership. Of course, it is
possible that A and B may jointly bid for the asset but restructure ownership to yield a
more efficient outcome. When there are markets for ownership, such restructuring is
more complex. That possibility will be discussed in Section 4 below.
3. The Possibility of Resale
The property rights approach to the theory of the firm emphasises the
characteristic of ownership that asset owners have residual rights of control as to the use
to which an asset is put. Ownership is a source of power in that the owner can exclude
others from using (or profiting) from a particular asset. This limits the outside options of
others relative to the owner in any negotiations over the asset’s use. It is this feature of
ownership that generates the particular distribution of the ex post surplus in the model
considered in the previous section.
But another important right associated with ownership is the right to transfer
ownership of an asset to another agent. Such exchange rights play an important, implicit
role in the GHM approach as their allocation mechanism presumes that agents will

productive agent ownership) is less than (N-1)/(N+1), O-ownership remains the unique equilibrium.
18
In the previous numerical example, this condition holds as A does not make its investment under joint
ownership so that the surplus there is 180 of which A and B receive half each whereas A’s payoff under A-
ownership is 100 and B’s under B-ownership is 140 each below 270.
17
transfer control rights to generate an (constrained) efficient ownership structure. Their
allocation mechanism, however, assumes that all relevant agents can be party to the ex
ante ownership negotiation and that once fixed the owner either cannot (or does not have
the incentive to) transfer ownership to another agent.
Having explored the potential difference between market-based allocations of
ownership and efficient ones, this section now turns to consider the question of whether
agents allocated ownership in date 0 would continue to own the asset throughout the
investment, negotiation and production process. This question is addressed by analysing
an enriched model that gives an owner the opportunity to exchange ownership of the
asset with another agent. This can shed light on the ultimate equilibrium allocation of
ownership. For example, the GHM approach allocates ownership to a particular agent.
This section will consider whether that agent has an incentive to re-sell the asset. In
addition, the previous section has highlighted instances whereby an outside party may be
an asset’s initial owner. When does that agent have an incentive not to resell?
Constructing a model of resale is not a simple matter, however. Since Coase
(1960), a central insight of the property rights approach is that ownership matters for the
distribution of rents. So individual agents will not be indifferent as to who owns an asset.
This was highlighted in the discussion in the previous section whereby productive agents
preferred ownership by the other productive agent than an outside party. Indeed, it was
externalities of this type that drove the equilibrium of that model. Such externalities will
play a role in a model of resale and make it difficult to characterise asset market
18
equilibria.
19
For this reason, the focus here is on the questions motivating this paper
rather than a complete characterisation of asset market equilibria.
It should also be noted that, at this stage, attention is restricted to exchange
models that do not allow the asset seller to limit the future re-sale opportunities of any
buyer. This is an important restriction in that buyers cannot commit to abstain from
imposing negative externalities on the seller during future resale negotiations. However,
one can imagine sale contracts that prevent the buyer from reselling to another agent or
agent type. Such contractual restrictions will be considered in the next section.
A Model of Resale
Suppose that any owner of an asset can potentially sell the asset at any time
before date 1, when the productive agents take their non-contractible actions.
20
Between
dates 0 and 1, the time allowed for re-selling is infinite and there is no discounting. It is
assumed that an asset-owner has an opportunity to sell the asset with probability, p.
Otherwise, with probability 1-p, the asset-owner is forced to produce – moving to dates 1
and 2. Thus, re-sale opportunities are limited but symmetric across agents.
When an opportunity to re-sell arises, each non-asset-owner makes a
simultaneous take-it-or-leave-it offer to the current owner. That owner then decides if and
to whom they sell the asset. If they do not sell, they produce and all agents receive their

19
There is an emerging literature that considers auctions and negotiations when there are externalities
between different sellers and buyers. See, for example, Jehiel and Moldovanu (1995, 1996, 1999), Jehiel,
Moldovanu and Stacchetti (1996), Calliaud and Jehiel (1998) and Segal (1999).
20
In principle, resale should be able to occur after that point and such exchange will have a material impact
on resulting payoffs to agents. However, for the moment, attention is confined to re-sales in the ex ante
asset market. Ex post asset sales (between dates 1 and 2) will serve to impact on the distribution of ex post
rents. However, in many respects, these distributional issues are already captured in the Shapley value
calculation.
19
payoffs. If they sell, a payment is made and the game begins again with the new owner
being able to re-sell with probability p. Thus, the exchange mechanism considered here
gives all the bargaining power to the buyer
21
and also has an inbuilt delay. Note,
however, that it is equivalent to a discriminatory price auction whereby the seller takes
into account the identity of the buyer when determining the overall sale price.
22

Nonetheless, agents are not permitted to collude in the sale process.
Finally, it is convenient to adopt a notational change in this section. In particular,
let
i
j
π be the (overall) payoff to agent j if agent i is the owner at date 1. These payoffs
correspond to the payoffs in Table 3. Also, suppose that A is the efficient owner. In this
case, recall that:
A A B B O O O
A B A B A B O
π π π π π π π + ≥ + ≥ + + ,
A B O
A A A
π π π ≥ ≥ and
B B O
B A B
π π π ≥ ≥ .
When Will the Outside Party Choose to Produce rather than Re-sell?
Consider a situation where an outside party owns the asset. Given the model of
resale specified here, will that agent sell the asset to either A or B? If O does not sell, then
an allocation of ownership to them will ‘stick,’ leading to less value creation than even
the second-best situation considered in the incomplete contracts literature.
23


21
This is for convenience only and to provide consistency with the bidding model of the previous section.
Many of the results here are easily generalisable to a model of exchange whether the seller has all of the
bargaining power or there is some allocation of power among agents.
22
If the sale mechanism were a non-discriminatory price auction where the seller sold the asset to the
bidder submitting the highest bid and could not identify that bidder, then the equilibrium owner would be
the same as that in the model without re-sale considered above.
23
Bolton and Whinston (1993) consider a similar form of re-sale and equilibrium. They allow owners to
engage in a potential sequence of trades but similar to the model here do not allow sellers to pre-determine
the future paths of sales. They do, however, potentially allow multi-lateral exchange agreements; while
here I restrict attention to bilateral agreements. They then consider when a particular ownership structure
will be ‘quasi-stable’ in that that owner has no path of trades that guarantees them a higher payoff than
holding on to the asset. They find, in particular, that single agent ownership of all assets is quasi-stable
whenever it is socially optimal. This is because no coalition of other agents could generate a transfer large
enough to give effect even to a single trade of the asset as the surplus generated would fall in that event.
However, if there exist an outside party (or nearly outside party), this paper has demonstrated that such a
20
It is interesting to consider, first, how O might be able to earn more from re-sale
than from production. Recall that if either A or B expect to produce with the asset rather
than re-sell themselves, and the conditions of Corollary 1 hold (as will be assumed here)
their willingness-to-pay for ownership will be less than O’s payoff from production.
Similarly, if only one productive agent expects to produce (while the other re-sells),
under the bidding model assumed here, O will be unable to earn more than their
production payoff by selling.
O can potentially earn more, however, if both A and B are interested in re-selling
the asset. To see this, note that if B has the asset then potentially it can earn more rents by
re-selling to A. Competitive bidding from O will push that sale price to
A O
A A
π π − which
leaves A indifferent between its own production and O-ownership, while B potentially
earns
A A O
A B A
π π π + − if A holds on to the asset. Thus, B can potentially appropriate all of
the rents from A-ownership. Moreover, by purchasing the asset, B avoids being re-sold to
by A (where A would appropriate more rents). The negative externality arising from
potential re-sales to each other is something O can use to appropriate a greater bid price.
The following proposition demonstrates that O-ownership will ‘stick’ whenever
the rents O can appropriate from bidding competition between A and B are low.
Proposition 3. Suppose (1)
( )
2
(1 )
O O O B
A O B B
p p π π π π < − + − or (2)
( )
2
(1 )
O O O A
B O A A
p p π π π π < − + − . Then it is a subgame perfect equilibrium for O not to sell.

The proof is in the appendix. Basically, the condition of the proposition requires that A
and B’s payoffs under O-ownership are small and there are relatively few re-sale

trade is possible.
21
opportunities.
24
The left hand side of each inequality represents the ‘bargaining position’
the other productive agent will have in any subsequent re-sales. Using the information
from Table 3, this translates into a situation where the value created when A and B
produce without the other are sufficiently low. If this is high, then an agent will bid more
intensively for ownership to avoid being in a relatively weak bargaining position at a later
stage. Of course, this is only a concern if re-sale opportunities arise frequently (high p)
and if productive agents can credibly threaten to re-sell to O (i.e., the conditions of
Corollary 1 that form the right hand side of the inequality). Therefore, so long as re-sale
opportunities are sufficiently low, bidding between A and B will not give rise to rents to
O that outweigh O’s expected payoff from production.
Note that, under the conditions of Proposition 3, in ex ante bidding for the asset,
O will be allocated the asset. This is because the most A or B are willing to pay for the
asset are
( )
(1 )
A O O O
A O A A
p p π π π π − + + − and
( )
(1 )
B O O O
B O B B
p p π π π π − + + − , respectively,
each of which is less than
O
O
π . Thus, in these circumstances, the model has a clear
prediction of outside ownership.
When Will the Efficient Owner Choose to Re-Sell rather than Produce?
Proposition 3 demonstrates that it is possible for an outside party, allocated asset
ownership, to choose to produce rather than re-sell the asset to a productive agent (under
whose ownership greater value will be generated). What, however, will happen in the
alternative scenario whereby the efficient ownership structure is chosen ex ante but there
is an opportunity for the owner, in this case A, to re-sell the asset? Under what conditions

24
For our earlier numerical example, these conditions would be satisfied if p < 0.2087.
22
will A choose to re-sell the asset instead of producing with it; thereby, risking a situation
(because re-sale opportunities are potentially limited) that another agent owns the asset
during dates 1 and 2.
The model of re-sale assumed here leads to a striking result that, under the
conditions in Corollary 1 (with respect to the market without re-sales), A will always
choose to re-sell the asset rather than hold on to it. This is a direct implication of the
following proposition:
Proposition 4. Suppose that A owns the asset. If the conditions of Corollary 1 hold, then
retaining ownership is dominated by re-selling to O.

The proof is in the appendix. This proposition also applies to B. Hence, neither A nor B-
ownership will ‘stick’ under the conditions of Corollary 1. The intuition is
straightforward. A will always be able to guarantee a price for the asset of
O
O
π because of
competition between O-types. On the other hand, if the new owner re-sells there is a
potential negative effect imposed on A. However, regardless of this A can always
guarantee a minimum payoff following re-sale of
O
A
π ; as if O-ownership continues. This
is because A can always refuse to purchase the asset in subsequent rounds (if they arise)
thereby leaving the only equilibrium productive options O or B ownership resulting
O
A
π
or
B
A
π respectively.
Proposition 4 demonstrates that, even if ownership resides with the GMH-
efficient owner, that owner will have an incentive to re-sell the asset if the opportunity
arises. This means that there is a positive probability that production will not occur with
that agent as the owner. Hence, the equilibrium will not be efficient.
23
Finally, it is interesting to examine the conditions under which ownership might
cycle between A and B as a subgame perfect equilibrium. Suppose that the conditions of
Proposition 3 holds so that O-ownership will ‘stick’ if O ever becomes the owner. If it
has ownership, A will sell to B only if:
( )
( ) ( ) ( ) ( )
(1 )
(1 ) (1 )
B O O O
B O B B
O O B A O O O O
O A A A O A O B
p p
p p p p
π π π π
π π π π π π π π
− + + −
> + − − + − + + − +

( ) ( )
2
(1 ) (1 ) (1 )
B B A O O O
B A A O A B
p p p p π π π π π π ⇒ − + + − > − + + (1)
Symmetrically, B will sell to A only if:
( ) ( )
2
(1 ) (1 ) (1 )
A A B O O O
A B B O B A
p p p p π π π π π π − + + − > − + + (2)
Both of these together imply that
( ) ( ) ( ) ( )
2 2
(1 ) (1 ) 2 2
A B A B O O O O O O
B A A B O A B O A B
p p p π π π π π π π π π π − + + − + > + + − + + .
Thus, a necessary condition for this to hold is that
( )
(1 )
A B O O
B A A B
p π π π π − + > + .
Obviously this will hold not hold if p = 1. However, if p is low, a cyclic equilibrium is
possible.
25


25
The initial owner will depend upon whose willingness to pay is higher. For B’s willingness to pay to
exceed A’s requires:
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
2 2 2 2
(1 ) (1 ) (1 )
(1 ) (1 ) (1 )
(1 ) (1 ) (1 ) (1 )
B O O A B O O O O
B O B B B O B O A
A O O B A O O O O
A O A A A O A O B
B B O A A O
B A B A B A
p p p p p p
p p p p p p
p p p p p p
π π π π π π π π π
π π π π π π π π π
π π π π π π
− + + − − + − + + − +
> − + + − − + − + + − +
⇒ − + − − > − + − −

a condition that may or may not hold. Note that the conditions supporting a cyclic equilibrium become
stronger when there is the possibility of intense bidding between A and B; i.e., when O-ownership does not
‘stick.’ This type of equilibrium is a feature of models of exchange of indivisible objects with externalities
(Jehiel and Moldovanu, 1995).
24
Contractual Limits on Re-Sale
The re-sale model considered here does not permit the asset-seller to impose
conditions on the buyer. In particular, it does not restrain a buyer from re-selling (or re-
selling where it is efficiency-improving to do so). As Bolton and Whinston (1993) note,
such restrictions on future exchange may be difficult specify contractually. However, it is
useful to consider the implications of an alternative assumption; whereby at the time of
sale contractual restrictions on future re-sale can be specified.
An interesting question is whether parties would have an incentive to agree to
restrictions on future sales. Such restrictions remove an option, thereby reducing a
potential buyer’s willingness-to-pay for ownership.
26
On the other hand, a restriction can
remove the potential negative externality that might be imposed on an asset-seller in
future re-sale transactions. Thus, restrictions on later re-sale may lower or raise the gains
from asset trading.
In a situation where asset ownership is expected to stick with a potential buyer,
contractual restrictions on re-sale do not bind. This will occur for O as a buyer under the
conditions of Proposition 3. However, consider the roles of A or B as buyers. If, say, A is

26
Such options can play an important role in ex post rent division. Consider a situation where ownership
has been assigned to the GHM-efficient agent (say A) prior to date 1 and non-contractible actions have been
taken. In this situation, ex post asset trading cannot alter the overall surplus that will be generated; only its
division. Thus, the appropriate world is akin to the complete contracting environment considered in Section
2. In this environment, A, if it has a re-sale opportunity will be able to guarantee itself
( )
2 1 1
3 6 2
( , ) ( ) ( ) ( , ) ( )
A B A
v a b v a v b v a b v a + − > + (or
O O A
O A A
π π π + > ); whereas B will receive
( )
1 1 1 1
3 2 3 6
max ( , ) ( ) ( ) , ( , ) ( ) ( )
A B A B
v a b v a v b v a b v a v b ] − + − +
]
.
Notice that, if this occurs, then A’s ex ante incentive to undertake its non-contractible investments
will be higher, whereas B’s investments may be higher or lower. The option to re-sell the object means that
A will expect surplus higher than that implied by a pure Shapley value calculation. To the extent, that A’s
investment is ‘important’ or perhaps A is the only agent with a non-contractible action, then surplus will be
higher than expected under the GHM approach.
25
the seller, then the gains from trade with B are
B O B O O
B B A A O
π π π π π − + − − . Subtracting this
from the gains from trade in (1) gives:
( ) ( ) ( ) ( )
( )
(1 ) 0
(1 )
B O O B A O O O O
B O B A A O A O B
A O O B B
A O A B A
p p p p p p
p p
π π π π π π π π π
π π π π π
− + + − + − + + − + >
⇒ − + + > +

This inequality never holds under our key assumptions. Hence, A and B will find it
optimal to place a restriction on re-sale by B.
Note, however, that an initial asset owner will not find it optimal to place
restrictions in re-sale. Therefore, this means that the willingnesses-to-pay of A and B for
the asset will be
( ) ( ) ( )
(1 ) (1 )
A O O B A O O
A O A A A O B
p p p p π π π π π π π − + + − − + − − and
( ) ( ) ( )
(1 ) (1 )
B O O A B O O
B O B B B O A
p p p p π π π π π π π − + + − − + − − ,
respectively (assuming that each has a willingness-to-pay in excess of O). Essentially, A
and B have less to fear from ownership by the other as future trade between them will
have higher gains from trade that in our case accrue to the buyer. Thus, their willingness-
to-pay for ownership is lower than is the case when re-sale restrictions are not possible;
increasing the likelihood the O will successfully bid for the object and that O-ownership
will ‘stick.’
At this point it is worthwhile to draw a comparison between the model of re-sale
in this paper and that of Jehiel and Moldovanu (1999) that was designed to analyse the
implications of re-sale in Coasian settings. Their model of re-sale has a finite horizon in
which opportunities for re-sale are unlimited. Their main result of interest for the present
paper is that the final assignment of ownership is efficient whenever there are three or
26
fewer traders.
27
Thus, in the environment of the present paper, the ultimate outcome
would be efficient with A ultimately owning the asset.
The key feature of their model driving the different conclusions drawn here is that
all agents know that re-sale opportunities will evaporate at a pre-determined date.
28
So
long as there are enough trading periods, those agents can always time their trades so that
the efficient owner is the last buyer at that date; hence, in their model, trades can be
structured so that the efficient buyer does not ultimately have a re-sale opportunity. For
example, B could own the asset at the penultimate period. The gains from trade between
it and A would be 0
A A O O O
A B O A B
π π π π π + − − − > . So whenever B owns the good it will be
in its interest to wait until the penultimate period and sell to A. In addition, if any other
agent owns the good before the penultimate period, then it is in their interest to sell to B
so it is the owner in that period. Thus, the only possible outcome is an efficient one.
The idea that there is a fixed time life for which re-sales could occur is interesting
and may be appropriate for some assets that have a finite life whose chief value is as an
option (say tickets to the Olympics). However, when discussing the theory of the firm, it
is more appropriate to consider asset life as potentially infinite and to provide restrictions
on re-sale that are symmetric across time. Nonetheless, even in the Jehiel and Moldovanu
approach, when there are more than three agents (say three productive agents and an
outside party), inefficient assignments are again possible.

27
See their Proposition 4.12.
28
Their model also has sellers making take-it-or-leave-it offers to buyers rather than receiving bids.
However, as all of the above results concentrate on gains from trade this distinction is immaterial.
27
4. Joint Ownership and Cooperative Bidding
Thus far, the analysis here has focused on situations where no cooperation was
possible in asset trading (whether initially or in re-sale markets). This assumption was
made to explore the equilibrium outcomes that arose when cooperation was not possible.
It is, therefore, appropriate at this stage to briefly consider when such a non-cooperative
assumption may be reasonable as opposed to the cooperative mechanism assumed by
GHM.
Joint Ownership
Suppose that productive agents could submit bids for joint ownership as well as
individual ownership. As demonstrated above, in general, this possibility will mean that
outside ownership is no longer an equilibrium outcome; although joint ownership (with
each agent having veto power over the asset’s use) could be an equilibrium.
Such joint ownership is never efficient in the GHM approach.
29
This inefficiency
suggests that the productive agents could enhance their payoffs by restructuring their
control rights; effectively assigning ownership in an efficient way. The difficulty here is
that that would require vesting ownership with a single agent who could then re-sell the
asset; imposing a negative effect on the other productive agent and potentially reducing
overall surplus. Indeed, Proposition 4 demonstrates that productive agents cannot commit
not to engage in such re-sales. This reduces the potential surplus from the re-structure
perhaps below that from joint ownership; especially if the productive agent sells to O and

29
See Hart and Moore (1990, Proposition 4).
28
that ownership ‘sticks.’ This lack of commitment would prevent a move from joint
ownership.
Of course, if the efficient owner were restricted from engaging in re-sales – as
part of the ownership re-structure – but still retained the right to exclude the other
productive agent from being associated with the asset, then efficient re-structuring could
occur. However, exclusion is not the only value from ownership and part of the rights
underlying the Shapley value division of ex post surplus could arise from other factors –
including the ability to re-sell the asset. In this situation, restricting re-sale may lead to an
inefficient outcome; although it may still be preferable to joint ownership. Even here,
however, there is an issue as to whether it would be possible to write a contract leaving
re-sale options in place but that prevented the owner from engaging in ex ante asset sales.
Cooperative Bidding
Suppose that prior to the initial auction of the asset, all of the productive agents
can get together and agree to a cooperative bid supported by side-payments so that a
specific agent becomes the asset’s owner. Suppose also that the ex ante side payments
internalise any potential externalities that might arise ex post or, equivalently, that the
supported ownership structure ‘sticks.’ Under these conditions, it will be in the interest of
the productive agents to agree to side-payments that allow the GHM-efficient owner to be
successful in the initial auction. This type of cooperative bidding could mimic the
outcome of the GHM allocation mechanism.
This raises the question, however, as to what situations it is reasonable to expect
that productive agents will be able to negotiate the side-payments that would support
29
such a cooperative bid. The analysis here has focused on a model with two productive
agents. In this situation, a cooperation bidding agreement between A and B is plausible.
Consider, however, a situation in which there were many productive agents. In this
situation, there are numerous results in multi-lateral bargaining suggesting the difficulties
of supporting an efficient outcome arising from a non-cooperative game.
30
These results
suggest that as the number of agents who are parties to a multi-lateral negotiation rises,
the more difficult it is for them to reach an efficient agreement.
To explore this point, here, I focus on the work of Dixit and Olson (2000) who
provide a model of multi-lateral agreements that most closely fits the environment of this
paper. They take, as a core assumption that any agreement reached must be ‘voluntary’ in
the sense that agents must have an option as to whether to participate in a multi-lateral
negotiation. In the context here, each productive agent would have an ex ante option to
participate or not in any cooperative bidding arrangement. However, it will be assumed
that if they choose to participate, there are no other impediments to a mutually value
maximising agreement being reached by participating agents. Thus, the model here
involves a participation stage whereby all productive agents choose whether to participate
in a cooperative bid or not followed by a stage where participating agents agree before
bidding in the initial asset auction at date 0.
Dixit and Olson demonstrate that several types of equilibria are possible in this
environment. This includes when N > 2, that no agent decides to participate in the
cooperative arrangement but also that a sufficient number, M (< N), choose to participate
to ensure an efficient outcome is reached. That latter type of equilibrium, however,

30
See Rob (1989), Mailath and Postlewaite (1990), Osborne and Rubinstein (1990), Milgrom and Roberts
(1992, p.303) and Cai (1999),
30
involves the resolution of a coordination problem to determine who participates and who
does not. Because of this, Dixit and Olson focus their attention on mixed strategy
equilibria where each agent participates with probability, q. This mixed strategy,
therefore, necessarily means that with some probability (i.e.,
!
!( )!
1 (1 )
N
n N n
N
n N n
n M
q q
−
−
·
− −
∑
) that the cooperative arrangement does not succeed; and the
outcome is inefficient.
The Dixit and Olson approach applies directly to the situation here. As is
demonstrated in the appendix, for the N productive agent case, there is a number, M,
strictly less than N of agents whose participation in a cooperative bid is sufficient to
guarantee that bid is successful over an outside agent. However, productive agents who
do not participate in the cooperative bid receive all of the benefits arising from a lack of
outside ownership while not having to contribute to the bid price itself. Hence, there is a
free riding problem and, moreover, as is demonstrated in the appendix, under certain
conditions, that free riding problem becomes more salient as N grows large. For larger
numbers of productive agents, the chance that any given agent is pivotal in ensuring the
success of a cooperative bid is small, and hence, each weighs the probability of their
participation lower in their chosen mixed strategy.
This suggests that the number as well as the importance of productive agents will
be important predictors of whether we see outside ownership in practice. However, the
issue of when cooperative outcomes will break down in favour of non-cooperative
outcomes remains an open area for further research and such analysis should yield more
testable implications as to when outside ownership will be observed.
31
5. Applications
In addition to demonstrating that outside ownership can be an equilibrium
outcome when ownership allocation is determined non-cooperatively, this paper has also
explored the instances when such equilibrium outcomes are likely to be observed. In
particular, outside ownership is more likely to be observed if (1) there exist substitute
instruments to ownership in providing incentives to productive agents; (2) there are many
‘small’ productive agents and an absence of key agents; (3) there are legal restrictions
against cooperative bidding in asset markets; (4) re-sale markets are illiquid; and (5) it is
difficult or otherwise costly to impose contractual restrictions on re-sale. However, the
issue of when a non-cooperative allocation mechanism offers superior predictions to a
cooperative one (as consider by GHM) remains an open issue.
Each of these factors emerges in the type of situations in which we observe
predominant outside ownership. For example, while the vast majority of establishments
are owned and controlled by productive agents, a greater proportion of production is
provided by corporations that are owned and controlled by passive investors and mutual
funds (Hansmann, 1996). The analysis here suggests that firms that require a smaller
number of productive agents providing complementary inputs will be more likely to
resolve the free-rider issues associated with cooperative bidding for assets than a larger
corporation with many productive agents. Consequently, more than efficiency and
incentive concerns may drive corporate mergers.
Alternatively, consider the processes involved in privatising the state-owned
enterprises in the former-Communist economies of Eastern Europe. While different
32
methods of privatisation were employed in these economies, the eventual owners of firm
assets were often outside parties such as mutual funds, rather than the managers of those
establishments. This occurred even where employees and managers were initially vested
with shares in those privatised firms. Some commentators have attempted to explain this
as an efficient means of re-structuring and renewing those enterprises (Boycko, Shleifer
and Vishny, 1995). However, it could also be the case that such patterns resulted from an
inability of productive agents to form effective coalitions preventing sales to outside
parties or legal restrictions banning collusion among those agents in asset auctions.
Finally, it has been argued that venture capitalists provide important resources to
start-up firms such as networking and commercial pressure as well as capital such
entrepreneurs might not otherwise have (Gompers and Lerner, 1999). These resources
overcome the potential reduction in efficiency that might otherwise be expected from a
reduction in entrepreneurial equity (Aghion and Tirole, 1994). However, consider Jim
Clark (formerly of Silicon Graphics) founding Netscape or Steve Jobs (Apple’s co-
founder) founding Pixar. Each of these entrepreneurs received outside venture capital
finance despite the wealth and network connections of their founding entrepreneurs. This
suggests that a possible reason why entrepreneurial firms relinquish equity and control
(including through subsequent IPOs) may be in part driven by the high value that outside
parties place on having a claim to the future rents of such firms relative to that of
founding entrepreneurs who will always remain critical to value creation by such firms.
33
6. Conclusion
This paper has demonstrated that markets for ownership can be important drivers
of the location of firm boundaries. Such markets tend to allocate ownership on the basis
of the relative private values different types of agent receive from ownership. While the
relative private values from ownership can themselves be determined by the incentive
effects arising from changes in bargaining position such effects need not dominate in the
face of complementarities that strengthen productive agents’ bargaining positions with
respect to outside parties. Consequently, while outside parties would never be allocated
ownership on efficiency grounds, they remain significant in markets for ownership as
such parties only receive rents through ownership. Hence, their existence is likely to be
an important factor in explaining observed patterns of ownership.
The above analysis of markets for ownership also highlights the potential
complexity of interactions in those markets. Changes in ownership impose externalities
on other agents and this complicates our ability to generate precise predictions regarding
equilibria in asset markets. In addition, there is an interaction between resale
opportunities and incentives to undertake non-contractible investments; especially when
contractual constraints can be imposed on resale options. The results in this paper identify
these issues as an important area for future research in terms of the operations of markets
where externalities are present and on the precise role that exchange options afford asset
owners.
34
Appendix: Proof of Propositions

Proof of Proposition 1

First, observe that, because ( , ) v a b is supermodular,
A B
V V V > + ; i.e.,

( , ) ( , ) ( ,0) (0, )
A B
V v a b a b v a b a b v a v b a b V V ′′ ′′ ′′ ′′ ′ ′ ′ ′ ′ ′ ′ ′ · − − ≥ − − > + − − · + ,

where
,
( , ) argmax ( , )
a b
a b v a b a b ′′ ′′ ∈ − − , argmax ( )
a A
a v a a ′∈ − and
argmax ( )
b B
b v b b ′∈ − ). Second, note that O has a willingness-to-pay, and hence greatest
potential bid of ( )
1 1
3 2
( )
A B
V V V + + . This is because it does not earn any rents under other
ownership structures. Therefore, for the asset to be owned by another agent, their value of
ownership must exceed the amount they expect to earn under O-ownership. For B, this is
( )
1 1 1
2 3 2
( )
B A B
V V V V V + − − + and for A, this is ( )
1 1 1
2 3 2
( )
A B A
V V V V V + − − + ; both of which
equal ( )
1 1
6 3 A B
V V V + + . By the first observation, this amount is less than O’s maximum
bid. This proves O-ownership is an equilibrium.

For uniqueness, note that by the first observation, O’s maximal bid exceeds the
bid either A or B would make if they believed each other was the next highest bidder; that
is,
1
2
( )
A B
V V + .


Proof of Proposition 2 and Corollary 1

Corollary 1 is proven along a similar line to Proposition 1; comparing the
willingness-to-pay of A, B and O using the payoffs in Table 3. Setting the left-hand-side
of the inequalities in Corollary 1 to zero allows a derivation of the condition in
Proposition 2.


Proof of Proposition 3

If O does not sell, it receives
O
O
π . If it chooses to sell, there are several possible
scenarios. First, suppose that A and B each expect to produce if they purchase from O. In
this case, by the condition of the proposition, neither will be willing to pay more than
O
O
π
for ownership.

Second, suppose that B is expected to produce if they purchase from O but A will
re-sell if it has the opportunity. If A re-sells to O, because there are many such agents, A
will receive
O O
O A
π π + which is greater than its payoff from producing under (2). If A re-
sells to B, it will receive
O O
O A
π π + as B will place a bid that is just sufficient to leave A
indifferent between selling to B and O. Thus, in either case, A’s value from ownership is
35
( )
(1 )
A O O
A O A
p p π π π − + + . Therefore, A will not purchase from O if
( )
(1 )
A O O O O
A O A O A
p p π π π π π − + + ≤ + or
( )
(1 ) (1 )
A O O
A O A
p p π π π − ≤ − + which always holds
by the condition in the proposition. The proof where B is the purchaser instead of A is
analogous.

Third, suppose that B is expected to re-sell if they have the opportunity. In this
case, if B purchases from A, A will still receive
O O
O A
π π + as B will take into account any
potential external effect from its re-selling on its bid price to A. Thus, A’s willingness to
pay is the same as the previous case.

Finally, suppose that both A and B expect to re-sell (to each other) if given the
opportunity. Then O will receive the minimum of,

( ) ( ) ( ) ( ) ( )
(1 ) (1 ) (1 )
A O O B A O O O O
A O A A A O A O B
p p p p p p π π π π π π π π π − + + − − + − + + − + and
( ) ( ) ( ) ( ) ( )
(1 ) (1 ) (1 )
B O O A B O O O O
B O B B B O B O A
p p p p p p π π π π π π π π π − + + − − + − + + − +
So long as the minimum is less than
O
O
π , O will not sell. Suppose instead that both of
these are greater than
O
O
π . That is, for that associated with B’s willingness-to-pay,

( ) ( ) ( ) ( ) ( )
{
( )
2 2
2 2
2
(1 ) (1 ) (1 )
(1 ) (1 ) (1 ) (1 ) 0
(1 ) (1 ) (1 ) (1 ) 0
(1 )
O
B
B O O A B O O O O O
B O B B B O B O A O
B O O O A
B O B A B
B O O O A
B O B A B
O O O B
A O B B
p p p p p p
p p p p p p
p p p p p p
p p
π
π π π π π π π π π π
π π π π π
π π π π π
π π π π
>
− + + − − + − + + − + >
⇒ − − − + − + − − >
⇒ − − − + − + − − >
⇒ > − + −

Thus, if
( )
2
(1 )
O O O B
A O B B
p p π π π π < − + − the above inequality cannot hold and O will
choose to produce rather than re-sell. The condition
( )
2
(1 )
O O O A
B O A A
p p π π π π < − + − in the
proposition is derived symmetrically from A’s willingness-to-pay.


Proof of Proposition 4

The key to this proof is the observation that, regardless of the pattern of
subsequent re-sales, A can always guarantee itself at least
O
A
π . To see this suppose A has
sold the asset. Regardless of the price received, in subsequent periods, A can always
commit to a return of
O
A
π by simply refusing to bid for the asset. This means A will never
bid for the object unless they expect to earn at least
O
A
π (net of the price paid for the
object). Thus, we need only consider outcomes where O produces (giving A
O
A
π ), or O
36
sells to B. Note that by the condition in the proposition B will not buy from O if B expects
to produce. However, it could be the case that B sells to O so that the asset cycles
between B and O. However, in this case B would earn
( ) ( )
(1 ) (1 )
B O O
B B O B B O
X p p p p X X π π π · − + + − + − from ownership while O would earn
(1 )
O O
O O O
X p p π π · − + . No trade will take place between O and B unless
O
B O
X π < . That
is,

( ) ( )
( ) ( )
2
(1 ) (1 ) (1 ) (1 )
(1 ) 1 1
B O O O O
B O B O B
B O O
B O B
p p p p p
p p p
π π π π π
π π π
− + + + − < + −
⇒ − < − + −


which is always true by the condition in the proposition. Hence, A can always be
guaranteed
O
A
π .

Similarly, if it sells the object, A receives at least
O
O
π . Hence, A’s minimum
payoff from selling is
O O
O A
π π + which exceeds A’s payoff from production by the
condition in the proposition.
N-agent Case and Cooperative Bidding
Suppose that there are N symmetric productive agents and that if n are involved in
production value created is ( , ) v n a where a is a vector comprising the investment levels,
a
i
, chosen by the n participating agents. If n = 0, it is assumed that v = 0.

In this situation, if a productive agent owns the asset, its payoff is:

1
1
( , )
N
i i
i i
n
v n a
N
π
·
· −
∑
i
a (1)
whereas that for a productive agent ( j i ≠ ) who does not own the asset is:

1
1 1
( , ) ( , )
1
N
i i
j j
n
v N v n a
N N
π
·
| `
· − −

−
. ,
∑
i i
a a (2)
where
i
j
a is the chosen investment by j and
i
a is the vector of chosen investments under
i-ownership. In contrast, under outside ownership, each productive agent earns:

1
1 1
( , ) ( , )
1
N
O O O O
i i
n
v N v n a
N N
π
·
| `
· − −

+
. ,
∑
a a (3)
while the outside owner earns:

1
1
( , )
1
N
O O
O
n
v n
N
π
·
·
+
∑
a (4)
This is also the willingness to pay of an outside agent. In contrast, the willingnesses to
pay of a productive agent is:
37

1 1
1 1 1
( , ) ( , ) ( , ) ( )
1
N N
i O O O i O
i i i i
n n
v n v N v n a a
N N N
π π
· ·
| `
− · − − − −

+
. ,
∑ ∑
i
a a a (5)
If
O i O
O i i
π π π − + is positive, outside ownership is the unique equilibrium. This requires:

1 1
1 1 1
( , ) ( , ) ( , ) ( ) 0
1
N N
O O i O
i i
n n
N
v N v n v n a a
N N N
· ·
− | `
+ − + − >

+
. ,
∑ ∑
i
a a a (6)
If each productive agent is indispensable (i.e., ( , ) 0 for v n n N · < a ) then this condition
becomes:

2 1
( , ) ( , ) ( ) 0
1
O i O
i i
v N v N a a
N N
− + − >
+
i
a a (7)
Thus, a sufficient condition for outside ownership to be the unique equilibrium becomes
( , ) ( , ) 1
1
( , )
O
O
v N v N N
N
v N
− −
+
<
i
a a
a
. This condition is stronger than the condition derived when N = 2.
Thus, ceteris paribus, an outside ownership equilibrium is more likely the greater the
number of productive agents.

Notice that the difference
O i O
O i i
π π π − + is the shortfall in the bid of a productive
agent for the asset. If this shortfall is overcome then the overall gain to productive agents
as a group is:

1
1
( , ) ( , ) ( , )
1
N
O O O
n
v N v N v n
N
·
′ ′ − − + +
+
∑
i i
a I a a I a a (8)
which is strictly greater than
O i O
O i i
π π π − + whenever this is positive. This illustrates the
gain from cooperative bidding. Suppose that n productive agents choose to participate in
such a bid. A fair division of the surplus arising from that bid would equate the expected
surplus of the eventual owner with any of the other participants. That is, the participants
would each contribute t to the designated owner, determined by:
( 1) subject to ( 1)
i O i O i O
i O j O i i
n t t n t π π π π π π − + − · − − + ≤ − (9)
Solving for t and substituting into the constraint yields a value for M, the minimum
number of productive agents required for a successful cooperative bid:

( )
1
1
i O i
j O i i O i
j O i n i O
j i
t M M
π π π
π π π
π π
+ −
· + − ⇒ ≥ > −
−
(10)
Notice that M is independent of the number of participating agents although a given
productive agent’s payoff from participation is not. Hence, this exhibits the same free
riding property that characterises the Dixit and Olson (2000) results.

Of interest here, however, is whether, as the number of productive agents (N)
rises, the difficulties of achieving a cooperative outcome diminish. For Dixit and Olson,
the total value created was linear in the number of agents. Here, however, because of
complementary, an additional productive agent involves an increased marginal
contribution to overall surplus. Thus, surplus is higher as the number of productive agents
expands. The key question, however, is whether the minimum number of agents required
to support a cooperative bid rises more slowly than the increase in the number of agents.
This is a difficult question to analyse for the general case here. However, if we suppose
38
that productive agents are indispensable and their investments are non-contractible it is
easy to see that / ( , ) M N v N ≅ a . Given the complementarities, average product rises with
N. In this case, as N grows, M falls. According to Dixit and Olson’s calculations, this
makes a cooperative outcome less likely.
39
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