Stochastic Games on a Multiple Access Channel

TL;DR

This paper models a multi-user access channel as a stochastic game where users independently optimize their transmission strategies based on local information, analyzing equilibrium solutions and their properties.

Contribution

It formulates the multi-user access problem as a Markov game and develops algorithms to find equilibrium strategies under various throughput functions.

Findings

Equilibrium strategies can be computed using the proposed algorithms.

The model captures both saturated and unsaturated user scenarios.

Connections between Markov games and strategic form games are established.

Abstract

We consider a scenario where N users try to access a common base station. Associated with each user is its channel state and a finite queue which varies with time. Each user chooses his power and the admission control variable in a dynamic manner so as to maximize his expected throughput. The throughput of each user is a function of the actions and states of all users. The scenario considers the situation where each user knows his channel and buffer state but is unaware of the states and actions taken by the other users. We consider the scenario when each user is saturated (i.e., always has a packet to transmit) as well as the case when each user is unsaturated. We formulate the problem as a Markov game and show connections with strategic form games. We then consider various throughput functions associated with the multiple user channel and provide algorithms for finding these equilibria.