A Game-Theoretic Model for Medium Access Control ∗ (Invited Paper) Lijun Chen, Tao Cui, Steven H. Low, and John C. Doyle Division of Engineering and Applied Science California Institute of Technology Pasadena, CA, USA 91125 {chen@cds., taocui@, slow@, doyle@cds.}caltech.edu ABSTRACT In this paper, a game-theoretic model for contention based medium access control (contention control) is proposed. We define a general game-theoretic model, called random access game, to capture the distributed nature of contention control and the interaction among wireless nodes with contention-based medium access. We study the design of random access games, characterize their equilibria, study their dynamics, and propose distributed algorithms to achieve the equilibria. This provides a unique perspective to understand exist- ing MAC protocols and a general framework to guide the design of new ones to improve the system performance. As examples, a series of utility functions is proposed for games achieving the max- imum throughput in a network of homogeneous nodes. The con- vergence of different variants (e.g., asynchronous and stochastic algorithms) of different dynamic algorithms such as gradient play are obtained. An equilibrium selection algorithm is also proposed to guarantee that the dynamic algorithms can actually achieve the desired operating point. Simulation results show that game model based protocols can achieve superior performance over the stan- dard IEEE 802.11 DCF, and comparable performance as existing protocols with the best performance in literature. Categories and Subject Descriptors C.2.5 [Computer-Communication Networks]: Local and Wide- Area Networks—Access schemes General Terms Algorithms, Performance ∗ This work is partially supported by NSF through grants CNS- 0435520 and CCR-0326554, and Caltech’s Lee Center for Ad- vanced Networking. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. WICON ’07, October 22-24, 2007, Austin, Texas, USA Copyright 2007 ACM 987-963-9799-04-2/07/10 ...$5.00. Keywords Medium access control, Game theory, Nash equilibrium, Strategy update mechanism, Fairness, Wireless LANs. 1. INTRODUCTION Wireless channel is a shared medium that is interference-limited. A contention-based medium access control (contention control) is a distributed strategy to access and share a wireless channel among competing wireless nodes. It dynamically adjusts channel access probability in response to the amount of contention in the network. Note that the amount of contention itself depends on the channel ac- cess probabilities chosen by the wireless nodes. Hence contention control is a distributed, iterative feedback system described mathe- matically as: pi (t + 1) = Fi (pi (t),qi (t)), qi (t)= Ci (p(t)), (1) where pi (t) is the channel access probability of node i, p(t)= (pi (t)) is the corresponding vector, and qi (t) is certain measure of contention observed by node i that depends on the vector p(t). The channel access probability pi (t) is usually implemented either through a backoff algorithm on contention window or as a persis- tence probability. For example, the standard IEEE 802.11 DCF has a backoff algorithm that induces a channel access probability and can be modeled by some function F i . The algorithm responds to whether there is a collision, and hence the measure of contention q i (t) in 802.11 DCF is the probability of collision whose depen- dence on the channel access probability vector p(t) can be mod- elled by some function Ci . The performance of a MAC, e.g., the throughput, fairness and collision, depends critically on the equilibrium and stability of the dynamical system defined by (1). In this paper, extending from [7] we propose a game-theoretic model to understand the dynamical system (1), use it to design new classes of MAC, and present simu- lation results that demonstrate its superior performance over 802.11 DCF. Specifically, in Section 3, we propose a general random ac- cess game to model MAC protocols. The key idea is to consider each node i to have a utility function Ui (pi ) as a function of its channel access probability pi . The goal of node i is to maximize its payoff function ui (p) := Ui (pi ) − pi qi given the contention measure qi . Hence, the steady state properties of a MAC can be an- alyzed or designed through the specification of the utility function U i (p i ) and the choice of the contention measure q i (e.g., collision probability, or idle time between channel access, etc). Their spec- ification defines the underlying random access game whose equi-