Spectrum Trading with Insurance in Cognitive Radio Networks
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1 Spectrum Trading with Insurance in Cognitive Radio Networks 1/46 Spectrum Trading with Insurance in Cognitive Radio Networks Haiming Jin 1, Gaofei Sun 1, Xinbing Wang 1 and Qian Zhang 2 1 Department of Electronic Engineering Shanghai Jiao Tong University, China 2 Department of Computer Science and Engineering Hong Kong University of Science and Technology, Hong Kong March 29, 2012
2 Spectrum Trading with Insurance in Cognitive Radio Networks 2/46 Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
3 Spectrum Trading with Insurance in Cognitive Radio Networks 3/46 Motivations Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
4 Spectrum Trading with Insurance in Cognitive Radio Networks Motivations Motivations I The transmission between a secondary Rx and Tx is successful if the SINR at the Rx satisfies: γ= Recieved power α N0 + Is s + Ip s 4/46
5 Spectrum Trading with Insurance in Cognitive Radio Networks Motivations Motivations I The transmission between a secondary Rx and Tx is successful if the SINR at the Rx satisfies: γ= Recieved power α N0 + Is s + Ip s I γ < α = Transmission failure. 4/46
6 Spectrum Trading with Insurance in Cognitive Radio Networks 5/46 Motivations Motivations Negativity of transmission failure on spectrum efficiency: A secondary user s utility: ( u1, if γ α (Successful transmission) u = u 2, if γ < α (Failed transmission) A secondary user s expected utility: E{u} = `1 p{γ < α} u 1 + p{γ < α}( u 2) Potential transmission failure undermines spectrum efficiency, since it makes SUs better off if they do not partake in spectrum trading.
7 Spectrum Trading with Insurance in Cognitive Radio Networks 6/46 Motivations Motivations Can insurance be the solution to alleviate such a negative effect? Examples: travel insurance, home insurance, auto insurance and.
8 Spectrum Trading with Insurance in Cognitive Radio Networks 7/46 Motivations Motivations With insurance contract C = (λ, θ): A secondary user s utility: ( u u1 λ, if γ α = θ u 2, if γ < α A secondary user s expected utility: E{u } =`1 p{γ < α} (u 1 λ)+ p{γ < α}(θ u 2) >E{u}?
9 Spectrum Trading with Insurance in Cognitive Radio Networks 8/46 Related Previous Works Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
10 Spectrum Trading with Insurance in Cognitive Radio Networks 9/46 Related Previous Works Related Previous Works Lingjie Duan et al., INFOCOM 2010 [5] and TMC 2011 [11] Utilize Stackelberg game to study the investment and pricing for a Cognitive-Mobile Virtual Network Operator (C-MVNO). Compared with the traditional MVNO, spectrum sensing improves the C-MVNO s expected profit and users payoffs. Lin Gao et al., JSAC 2011 [8] Use contract theory to analyze spectrum trading in CRNs. Derive incentive compatible and individual rational contract that maximizes PO s revenue. Dusit Niyato et al., TMC 2009 [12] Incorporate evolutionary game theory to analyze multi-buyer and multi-seller spectrum trading in CRNs.
11 Spectrum Trading with Insurance in Cognitive Radio Networks 9/46 Related Previous Works Related Previous Works Lingjie Duan et al., INFOCOM 2010 [5] and TMC 2011 [11] Utilize Stackelberg game to study the investment and pricing for a Cognitive-Mobile Virtual Network Operator (C-MVNO). Compared with the traditional MVNO, spectrum sensing improves the C-MVNO s expected profit and users payoffs. Lin Gao et al., JSAC 2011 [8] Use contract theory to analyze spectrum trading in CRNs. Derive incentive compatible and individual rational contract that maximizes PO s revenue. Dusit Niyato et al., TMC 2009 [12] Incorporate evolutionary game theory to analyze multi-buyer and multi-seller spectrum trading in CRNs. Common assumption: Secondary Rxes operate at sufficiently high SINR.
12 Spectrum Trading with Insurance in Cognitive Radio Networks 10/46 Contributions Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
13 Spectrum Trading with Insurance in Cognitive Radio Networks 11/46 Contributions Contributions Appropriate formulation of the market game when we incorporate insurance mechanism into spectrum trading. Equilibrium analysis of the market game: Derivation of PUs insurance contract proposal strategies. Derivation of SUs insurance contract selection strategies. Analysis of the extent to which insurance mechanism can improve spectrum efficiency: Comparison of SUs utilities in cases with and without insurance.
14 Spectrum Trading with Insurance in Cognitive Radio Networks 12/46 Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
15 Spectrum Trading with Insurance in Cognitive Radio Networks 13/46 Network Model Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
16 Spectrum Trading with Insurance in Cognitive Radio Networks 14/46 Network Model Network Model Primary Network consists of one primary base station and m subscribed primary users. Secondary Network consists of n secondary transceiver pairs, i.e., {Tx k -Rx k } n k=1 operating on spectrum bands purchased from PUs.
17 Spectrum Trading with Insurance in Cognitive Radio Networks 15/46 Network Model Network Model Recieved power We assume that I p s differentiates the SINR, γ = N 0+I s s+i p s at secondary Rxes, hence we divide SUs into different types according to their distances d with the primary base station. d I p s γ Probability of transmission failure
18 Spectrum Trading with Insurance in Cognitive Radio Networks 16/46 Hybrid Market Structure Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
19 Spectrum Trading with Insurance in Cognitive Radio Networks 17/46 Hybrid Market Structure Multi-stage Trading Procedure
20 Spectrum Trading with Insurance in Cognitive Radio Networks 18/46 Hybrid Market Structure Risk Verification/Audition Definition. (Risk verification/audition) A primary user checks whether a particular secondary user cheats on its risk type with a certain probability and cost c.
21 Spectrum Trading with Insurance in Cognitive Radio Networks 19/46 Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
22 Spectrum Trading with Insurance in Cognitive Radio Networks 20/46 How do we formulate this market game as a Bayesian Game? 1. Players strategies. 2. Players beliefs. 3. Players utility functions. 4. Perfect Bayesian equilibrium (PBE). 5. Equilibrium allocation.
23 Spectrum Trading with Insurance in Cognitive Radio Networks 21/46 Players Strategies Stage I: PU i proposes insurance contract menu C i = (C i h, Ci l ) w.r.t. different types of SUs. Stage II: Any type-k (k {h, l}) SU chooses PUs contracts with probability distribution π k ( ) = ( π 0 kh ( ), π0 kl ( ),, πm kh ( ), πm kl ( )). Stage IV: PU i carries out risk verification with probability p i ( ). Assumption 1. Only two types of SUs exist, namely type-l and type-h SUs. Type-h SUs have higher probability of transmission failure than type-l SUs. Assumption 2. PUs propose identical channel price, τ i = τ, i {1,, m}.
24 Spectrum Trading with Insurance in Cognitive Radio Networks 22/46 Players Beliefs Definition. (Belief) The probability in PU i s belief that a claim for Cl i is from a type-h SU given the contract profile C: η i (C) = β h ξ h π i hl (C) β h ξ h π i hl (C) + (1 β h)ξ l π i ll (C), s.t. π i hl(c) + π i ll(c) > 0
25 Spectrum Trading with Insurance in Cognitive Radio Networks 23/46 SUs Utilities The expected utility of a type-l SU that purchases C i l: R ll (C i l) = (1 ξ l )r(u S τ λ i l) + ξ l r(u F τ + θ i l) ξ k, k {h, l} is the probability of transmission failure for type-k SUs. U S and U F are transmission reward in the case of successful and unsuccessful transmission. r( ) is concave. Similarly, we have R lh (C i h), R hh (C i h) and R hl (C i l).
26 Spectrum Trading with Insurance in Cognitive Radio Networks 24/46 SUs Utilities The expected utility of a type-l SU is: ( Λ l C, πl ( ) ) m ( = π i lh (C)R lh (Ch) i + πll(c)r i ll (Cl) i ) i=0 The expected utility of a type-h SU is: ( Λ h C, p( ), πh ( ) ) m = (πhh(c)r i hh (Ch) i + πhl(c)r i ( hl C i l, p i (C) )) i=0
27 Spectrum Trading with Insurance in Cognitive Radio Networks 25/46 PUs Utilities PU i s expected profit for C i l signed by a type-h SU is: G lh (C i l, p i) = (1 ξ h )λ i l ξ h`(1 pi)θ i l + p ic
28 Spectrum Trading with Insurance in Cognitive Radio Networks 25/46 PUs Utilities PU i s expected profit for C i l signed by a type-h SU is: G lh (C i l, p i) = (1 ξ h )λ i l ξ h`(1 pi)θ i l + p ic PU i s expected utility from an insurance contract is: Φ i`c, p( ), πh ( ), π l ( ) =β h πhh(c)g i hh (Ch) i + πhl(c)g i lh`ci l, p i(c) + β l πlh(c)g i hl (Ch) i + πll(c)g i ll (Cl, i p i(c)
29 Spectrum Trading with Insurance in Cognitive Radio Networks 25/46 PUs Utilities PU i s expected profit for C i l signed by a type-h SU is: G lh (C i l, p i) = (1 ξ h )λ i l ξ h`(1 pi)θ i l + p ic PU i s expected utility from an insurance contract is: Φ i`c, p( ), πh ( ), π l ( ) =β h πhh(c)g i hh (Ch) i + πhl(c)g i lh`ci l, p i(c) + β l πlh(c)g i hl (Ch) i + πll(c)g i ll (Cl, i p i(c) PU i s expected utility given that it has sold M channels and N insurance contracts is: Ω i`c, p( ), πh ( ), π l ( ), M, N =Mτ + NΦ i`c, p( ), πh ( ), π l ( )
30 Spectrum Trading with Insurance in Cognitive Radio Networks 26/46 Perfect Bayesian Equilibrium (PBE) Definition. (PBE) The perfect Bayesian equilibrium, E = C, p ( ), π h ( ), π l ( ), η ( ) satisfies: Ci is PU i s optimal contract proposal strategy given other PUs contract profile C i = (C1,, Ci 1, Ci+1,, Cm), and the continuation equilibrium strategy. π h ( ) and π l ( ) are SUs optimal contract selection strategies given p ( ). p i ( ) is PU i s optimal audition strategy given η i ( ). η i ( ) is calculated according to the Bayesian law.
31 Spectrum Trading with Insurance in Cognitive Radio Networks 27/46 Equilibrium Allocation Definition. (Equilibrium allocation) For any E = C, p ( ), π h ( ), π l ( ), η ( ), equilibrium allocation is C, p, π h, π l, η = C, p (C ), π h (C ), π l (C ), η (C ), i.e., players strategies played on the equilibrium path.
32 Spectrum Trading with Insurance in Cognitive Radio Networks 28/46 Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
33 Spectrum Trading with Insurance in Cognitive Radio Networks 29/46 Overall Procedure of Equilibrium Analysis Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
34 Spectrum Trading with Insurance in Cognitive Radio Networks 30/46 Overall Procedure of Equilibrium Analysis Overall Procedure of Equilibrium Analysis
35 Spectrum Trading with Insurance in Cognitive Radio Networks 31/46 Second-best Pareto Optimal (SBPO) Allocation Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
36 Spectrum Trading with Insurance in Cognitive Radio Networks 32/46 Second-best Pareto Optimal (SBPO) Allocation Feasible Allocation Definition. (Feasible Allocation) A feasible allocation C, p, π h, π l, η satisfies constraint C 1(β h, c, 0,, 0):
37 Spectrum Trading with Insurance in Cognitive Radio Networks 33/46 Second-best Pareto Optimal (SBPO) Allocation SBPO Allocation Definition. (SBPO Allocation) A feasible allocation {C, p, π h, π l } is Second-best Pareto optimal if no other feasible allocation {C, p, π h, π l } exists satisfying that: Λ k (C, p, π k) Λ k (C, p, π k ), k {h, l}
38 Spectrum Trading with Insurance in Cognitive Radio Networks 34/46 Second-best Pareto Optimal (SBPO) Allocation Approach of characterizing the SBPO allocation
39 Spectrum Trading with Insurance in Cognitive Radio Networks 35/46 Second-best Pareto Optimal (SBPO) Allocation Summary of Main Results in Theorems 1-4 Problem O 3: Players strategies depend on the combination of audition cost c and the probability that a secondary user is type-h β h, i.e., (c, β h ).
40 Spectrum Trading with Insurance in Cognitive Radio Networks 36/46 Second-best Pareto Optimal (SBPO) Allocation Summary of Main Results in Theorems 1-4 Problem O 2: If PUs carry out risk verification with positive probability, i.e., ṗ > 0, PUs and SUs strategies are demonstrated as follows.
41 Spectrum Trading with Insurance in Cognitive Radio Networks 37/46 Second-best Pareto Optimal (SBPO) Allocation Summary of Main Results in Theorems 1-4 Problem O 1 : The solution for problem O 1 (β h, c, ν 0, 0,, 0) coincides with that of problem O 2 (β h, c, ν 0, 0), when the maximum expected utility that a type-h SU can get from contract C i h or C i l (i {1 m}) is not equal to R hh( C h ).
42 Spectrum Trading with Insurance in Cognitive Radio Networks 38/46 Perfect Bayesian Equilibrium (PBE) Analysis Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
43 Spectrum Trading with Insurance in Cognitive Radio Networks 39/46 Perfect Bayesian Equilibrium (PBE) Analysis PBE Analysis Condition C 2 E satisfies C 2 if for the continuation sub-game after PUs propose the contract profile C, {p, πh, π l } is a trembling hand perfect Bayesian equilibrium (THPBE). Lemma. Any PBE allocation that satisfies C 2 coincides with the SBPO allocation.
44 Spectrum Trading with Insurance in Cognitive Radio Networks 40/46 Perfect Bayesian Equilibrium (PBE) Analysis PBE Analysis PBE E 1 in Region 3 Type-l SUs choose C l whereas type-h SUs randomize between C h and C l. PBE E 2 in Region 1 SUs select contracts designed for their own risk types.
45 Spectrum Trading with Insurance in Cognitive Radio Networks 41/46 Numerical and Simulation Results Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
46 Spectrum Trading with Insurance in Cognitive Radio Networks 42/46 Numerical and Simulation Results Numerical and Simulation Results Figure: Illustration of existence of E 1 Figure: Illustration of existence of E 2
47 Spectrum Trading with Insurance in Cognitive Radio Networks 43/46 Numerical and Simulation Results Numerical and Simulation Results Figure: Comparison of SUs utilities with and without insurance
48 Spectrum Trading with Insurance in Cognitive Radio Networks 44/46 Conclusion and Future Work Outline Motivations Related Previous Works Contributions Network Model Hybrid Market Structure Overall Procedure of Equilibrium Analysis Second-best Pareto Optimal (SBPO) Allocation Perfect Bayesian Equilibrium (PBE) Analysis Numerical and Simulation Results Conclusion and Future Work
49 Spectrum Trading with Insurance in Cognitive Radio Networks 45/46 Conclusion and Future Work Conclusion and Future Work Conclusion: Insurance can improve spectrum efficiency by alleviating the negative effect of transmission failure where high SINR cannot always be ensured. Some possible future directions: More complete derivation of several conclusions....
50 Spectrum Trading with Insurance in Cognitive Radio Networks 46/46 Conclusion and Future Work Questions? Thank you!
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