Market sharing games applied to content distribution in ad hoc networks

In third-generation (3G) wireless data networks, repeated requests for popular data items can exacerbate the already scarce wireless spectrum. In this paper, we propose an architectural and protocol framework that allows 3G service providers to host efficient content distribution services. We offload the spectrum intensive task of content distribution to an ad hoc network. Less mobile users (resident subscribers) are provided incentives to cache popular data items, while mobile users (transit subscribers) access this data from resident subscribers through the ad hoc network. Since the participants of this data distribution network act as selfish agents, they may collude to maximize their individual payoff. Our proposed protocol discourages potential collusion scenarios. In this architecture, the goal (social function) of the 3G service provider is to have the selfishly motivated resident subscribers service as many data requests as possible. However, the choice of which set of items to cache is left to the individual user. The caching activity among the different users can be modeled as a market sharing game. In this work, we study the Nash equilibria of market sharing games and the performance of such equilibria in terms of a social function. These games are a special case of congestion games that have been studied in the economics literature. In particular, pure strategy Nash equilibria for this set of games exist. We give a polynomial-time algorithm to find a pure strategy Nash equilibrium for a special case, while it is NP-hard to do so in the general case. As for the performance of Nash equilibria, we show that the price of anarchy-the worst case ratio between the social function at any Nash equilibrium and at the social optimum-can be upper bounded by a factor of 2. When the popularity follows a Zipf distribution, the price of anarchy is bounded by 1.45 in the special case where caching any item has a positive reward for all players. We prove that the selfish behavior of computationally bounded agents converges to an approximate Nash equilibrium in a finite number of improvements. Furthermore, we prove that, after each agent computes its response function once using a constant factor approximation algorithm, the outcome of the game is within a factor of O(log n) of the optimal social value, where n is the number of agents. Our simulation scenarios show that the price of anarchy is 30% better than that of the worst case analysis and that the system quickly (1 or 2 steps) converges to a Nash equilibrium.