Game-theoretic analysis of Markovian play order in wireless networks

Repeated games are a common tool for the analysis of communication networks; they consist of a number of consequent stage games. It is usually assumed that in each stage game, players play either simultaneously or in a predefined order. However, there can be found several situations, especially in wireless networks, in which the play order, e.g. the channel access order, is random. In this paper, we extend repeated games to address these new situations; we assume that the play order is determined using a positive recurrent Markovian transition matrix where the probability of selecting the next player/node depends on the current stage player. We call this kind of games repeated games with Markovian play order. After presenting a formal definition, we establish some necessary theorems leading to a Folk Theorem to show how and when cooperation is enforced in such games, and also present an extensive-form game. To better reflect applications of this model, we discuss its applications in some wireless networks in which the play order of nodes is Markovian; we evaluate a forwarding communication network and a token-based network as case studies and apply the obtained results to analyze the network against selfish nodes.