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Unformatted text preview: Pricing and Resource Allocation Game Theoretic Models Zhiyi Huang Changbin Liu Qi Zhang Computer and Information Science December 8, 2009 Z. Huang, C. Liu, and Q. Zhang (CIS) Game Theoretic Models December 8, 2009 1 / 20 Motivation The framework with prices ignores a number of issues that are important for analysis of resource allocation in largescale communication networks: 1 Centralized signals may be impractical or impossible 2 Prices are often set by multiple service providers with the objective of maximizing revenue We investigate the implications of profit maximizing pricing by multiple decentralized service providers. The model is of practical importance for a number of settings: 1 Transportation and communication networks 2 Markets in which there are snob effects Z. Huang, C. Liu, and Q. Zhang (CIS) Game Theoretic Models December 8, 2009 2 / 20 Example ` 1 ( x ) = x 2 / 3 ` 2 ( x ) = (2 / 3) x 1 unit of traffic 1 The efficient allocation that minimizes the total delay cost ∑ i ‘ i ( x i ) x i is x opt 1 = 2 / 3 and x opt 2 = 1 / 3 2 The equilibrium allocation that equates delay on the two paths is x eq 1 ≈ . 73 and x eq 2 ≈ . 27 The equilibrium of traffic assignment without prices can be inefficient. Z. Huang, C. Liu, and Q. Zhang (CIS) Game Theoretic Models December 8, 2009 3 / 20 Example (Cont’d) ` 1 ( x ) = x 2 / 3 ` 2 ( x ) = (2 / 3) x 1 unit of traffic 1 Monopolist will set prices p m 1 = (2 / 3) 3 and p m 2 = (2 / 3 2 ) . The resulting traffic in equilibrium will be x m 1 = 2 / 3 and x m 2 = 1 / 3 2 Duopoly situation results in p d 1 ≈ . 61 and p d 2 ≈ . 44 . The resulting traffic in equilibrium will be x d 1 ≈ . 58 and x d 2 ≈ . 42 Increasing competition can increase inefficiency Z. Huang, C. Liu, and Q. Zhang (CIS) Game Theoretic Models December 8, 2009 4 / 20 Intuition for the Inefficiency of Duopoly The inefficiency is related to a new source of monopoly power for each duopolist, which they exploit by distorting the pattern of traffic: 1 Provider 1 charges higher price 2 Some traffic is pushed from route 1 to route 2 3 The congestion on route 2 is raised 4 The remaining traffic on route 1 become more “lockedin” Z. Huang, C. Liu, and Q. Zhang (CIS) Game Theoretic Models December 8, 2009 5 / 20 Model We are interested in the problem of routing d units of flow across I links. 1 I = { 1 ,..., I } , set of links 2 x = [ x 1 ,..., x I ] , where x j denotes total flow on link j 3 ‘ j ( x j ) , a convex, nondecreasing, and continuously differentiable flowdependent latency function for each link j in the network, ‘ j (0) = 0 for all j 4 p j , price per unit flow of link...
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 Fall '09
 MichaelKearns
 Monopoly, Oligopoly, game theoretic models

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