Competition in cognitive radio networks: spectrum leasing and innovation

Competition in cognitive radio networks: spectrum leasing and innovation
CCNC 2011 Las Vegas, 11 January Luis Guijarro

Agenda
Objective Model Method Results and analysis Further work

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Objective
Spectrum leasing in a cognitive radio network To analyze equilibrium under competition between
Primary (PO) /incumbent and secondary (SO) /entrant operators
W-b b PO

p pp SO

ps

TU

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Model
Spectrum leasing PO leases b kHz to SO p and b are set outside the model Competition à la Bertrand
Strategies are pp and ps One-shot game
W-b b PO

p pp SO

ps

Quality of service
Spectrum W-b and b Spectral efficiency k(p) and k(s)
TU

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Model
Competition Income
n users Flat-rate

Costs
Operating costs

Profits

Π p = p p n p + p·b − C p Π s = p s n s − p·b − C s
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Model
Subscription Utility
⎛ ( p) W − b ⎞ ⎟ − p p = U p ( p p ,α ) U p ≡ log⎜ k ⎜ np ⎟ ⎝ ⎠ ⎛ (s) b ⎞ ⎟ − p s = U s ( p s ,1 − α ) U s ≡ log⎜ k ⎜ ns ⎟ ⎝ ⎠ np α≡ n
W-b b PO

p pp SO

ps

TU

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Method
Game theory
Multi-leader-follower game
The 2 operators fix their prices pi in order to maximize profits Each user subscribes to the operator which offers higher utility Ui

Solved by backward induction
First, solve subscription game Then, solve competition game anticipating the reaction by users.
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Method
Game theory
Multi-leader-follower game
Subscription game
• Wardrop equilibrium – Assume n is high enough – Equilibrium is reached when there is no incentive to change subscription decision • Assume that every user subscribe to service

U p ( p p , α ) = U s ( p s ,1 − α )
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Method
Game theory
Multi-leader-follower game
Competition game
• Nash equilibrium – The operator does not know the strategy chosen by the competitor, but space of available strategies are common knowledge
* p * = arg max Π p ( p p , p s ) p pp * p s = arg max Π s ( p * , p s ) p ps
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Results and analysis
Constant parameters
# of users, n Total spectrum W Leasing price p

Variable parameters
Leased spectrum b Spectral efficiency k(s)

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Results and analysis
Results
Market share α Prices pp, ps User utilities Up=Us Profits Πp, Πs Price of Anarchy PoA
Social welfare PoA
• the sum of the utilities of all agents in the system (npUp+nsUs+Πp+Πs) • the quotient between the maximum value of the social welfare and the social welfare obtained at the Nash equilibrium – i.e., PoA >=1

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Results and analysis
Impact of leased spectrum
Objective
Optimum amount of leased spectrum

Experiment
b/W varies from 10% to 90%

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Results and analysis
Impact of leased spectrum Results
Maximum user utility b/W≈0.45 Minimum PoA reached b/W≈0.35 Maximum profits would drive b/W towards 1

Conclusion
Maximum b should be fixed by regulatory authority
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Results and analysis
Impact of technology innovation
Objective
Impact of increasing k(s)

Experiment
k(s)/k(p) varies from 1 to 5

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Results and analysis
Impact of technology innovation
Results
User utility increases PoA tends to the unity

Conclusion
Users are better off when entrant innovates
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Further work
To model bargaining over the leasing price p and the leased spectrum b To model the user willingness to pay so that some users may decide to subscribe to neither PO nor SO

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