Zero-sum constrained stochastic games with independent state processes

Abstract

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player's controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints.

Stochastic games on a product state space: the periodic case

“…This kind of transition structure is natural, and has already been considered in applications. For applications in wireless networks, Altman et al (2005) (see also Altman et al 2007a,b) examined two-player product-games, although in a somewhat different fashion. They assumed that the sum of the payoffs is always equal to zero (zero-sum games), and dropped the assumption of full monitoring by letting each player observe only his own coordinate of the current state and the action chosen by himself.…”

A Jamming Game in Wireless Networks with Transmission Cost

“…These examples showed that Jammer pays less attention to the sub-channel with bad quality and Transmitter takes an opportunity to send some part of information over bad quality sub-channels. (2) and (3) we have that Proof of Lemma 1. (i1) For fixed ω > 0 and 0 ≤ ν 1 < ν 2 we have I 10 (ω, ν 1 ) ⊆ I 10 (ω, ν 2 ) and I 11 (ω, ν 1 ) ⊇ I 11 (ω, ν 2 ).…”

“…In [2] the authors have studied the application of dynamic stochastic zero sum game to the jamming problem in wireless networks. In the model of [2] the transmission power can be chosen from a discrete set.…”

“…In the model of [2] the transmission power can be chosen from a discrete set. Here we suppose that the power level can be chosen from a continuous set.…”

“…This formulation leads to a minimax problem. In the works [7] and [14] as well as in [2] the cost of transmission is not taken into account. Other problem formulations involving jamming in which one wireless terminal wishes to maximize the mutual information and the other tries to minimize it, can be found at [3].…”