We consider a non-cooperative constrained stochastic games with N players with the following special structure. With each player i there is an associated controlled Markov chain M DPi. The transition probabilities of the ith Markov chain depend only on the state and actions of controller i. The information structure that we consider is such that each player knows the state of its own MDP and its own actions. It does not know the states of, and the actions taken by other players. Finally, each player wishes to minimize a time-average cost function, and has constraints over other time-avrage cost functions. Both the cost that is minimized as well as those defining the constraints depend on the state and actions of all players. We study in this paper the existence of a Nash equilirium. Examples in power control in wireless communications are given.

Abstract-We consider the situation where N nodes share a common access point. With each node i there is an associated buffer and channel state that change in time. Node i dynamically chooses both the power and the admission control to be adopted so as to maximize the expected throughput, which depends on the actions and states of all the players, given its power and delay constraints. The information structure that we consider is such that each player knows the state of its own buffer and channel and its own actions. It does not know the states of, and the actions taken by other players. Using Markov Decision Processes we analyze the single player optimal policies under different model parameters. In the context of the stochastic games we study the equilibria of the N player scenario.

Abstract-In this contribution, the performance of a multi-user system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels for uplink CDMA. This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.

We study a finite population of mobiles communicating using the slotted ALOHA-type protocol. Our objective is the study of coordination between the mobiles in both cooperative as well as non-cooperative scenarios. Our study is based on the correlated equilibrium concept, a notion introduced by Aumann that broadens the Nash equilibrium. We study ways in which signaling can improve the performance both in the cooperative as well as in the non-cooperative cases, even in the absence of any extra information being conveyed through these signals.

Abstract-In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels. This scenario illustrates the case of decentralized schemes and aims at reducing the downlink signaling overhead. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large. To that end we combine two asymptotic methodologies. The first is asymptotic random matrix theory which allows us to obtain explicit expressions for the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games along with the Wardrop equilibrium concept which allows us to compute good approximations of the Nash equilibrium as the number of mobiles grow.

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In this contribution, the performance of an uplink CDMA system with random spreading and multi-cell interference is analyzed. A useful framework is provided in order to determine the base station coverage for wireless flat fading channels with very dense networks (in the number of users per meter) considering different receiver structures at the base station, namely the Matched filter, the Wiener filter and the Optimum filter. Using asymptotic arguments , analytical expressions of the spectral efficiency are obtained and provide a simple expression of the network capacity based only on a few meaningful parameters.

Abstract-A novel multi-user diversity scheme for OFDMA (Orthogonal Frequency Division Multiplexing Access) is described which alleviates the need of feedback and provides substantial improvements in non-cooperative environments. The algorithm exploits the reciprocity of the channel and enables a user to send reliably data at a prescribed rate knowing only its channel. Moreover, analytical expressions of the cell spectral efficiency are derived in the asymptotic regime (high number of carriers) for two filter types: matched filter and optimum filter. Discussions are also provided for various channel models.