Abstract-We study a problem where wireless service providers compete for heterogenous and atomic (non-infinitesimal) wireless users. The users differ in their utility functions as well as in the perceived quality of service of individual providers. We model the interaction of an arbitrary number of providers and users as a two-stage multi-leader-follower game, and prove existence and uniqueness of the subgame perfect Nash equilibrium for a generic channel model and a wide class of users' utility functions. We show that, interestingly, the competition of resource providers leads to a globally optimal outcome under fairly general technical conditions. Our results show that some users need to purchase their resource from several providers at the equilibrium. While the number of such users is typically small (smaller than the number of providers), our simulations indicate that the percentage of cases where at least one undecided user exists can be significant.
We study a problem where wireless service providers compete for heterogenous wireless users. The users differ in their utility functions as well as in the perceived quality of service of individual providers. We model the interaction of an arbitrary number of providers and users as a two-stage multileader-follower game. We prove existence and uniqueness of the subgame perfect Nash equilibrium for a generic channel model and a wide class of users' utility functions. We show that the competition of resource providers leads to a globally optimal outcome under mild technical conditions. Most users will purchase the resource from only one provider at the unique subgame perfect equilibrium. The number of users who connect to multiple providers at the equilibrium is always smaller than the number of providers. We also present a decentralized algorithm that globally converges to the unique system equilibrium with only local information under mild conditions on the update rates.
Abstract-We study the behavior of users in a classical Additive White Gaussian Noise Multiple Access Channel. We model users as rational entities whose only interest is to maximize their own communication rate, and we model their interaction as a noncooperative one-shot game. The Nash equilibria of the two-user game are found, and the relation between the purestrategy and mixed-strategy Nash equilibria is discussed. As in most games, the absence of cooperation and coordination leads to inefficiencies. We then extend our setting using evolutionary game theory, which we use to model a large population of users playing the MAC game over time. A unique evolutionary stable strategy is found for this case, corresponding to the strategy achieving the Nash equilibrium in a simplified one-shot game. Finally, we investigate what happens to the distribution of strategies in a population when we assume that the number of offsprings of a user is equal to the payoff of this user in a one-shot game. We find that the system converges to a state in which the average strategy of the population is the evolutionary stable strategy.
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