Reverse-Engineering MAC: A Non-Cooperative Game Model

Abstract

This paper reverse-engineers backoff-based random-access MAC protocols in ad-hoc networks. We show that the contention resolution algorithm in such protocols is implicitly participating in a non-cooperative game. Each link attempts to maximize a selfish local utility function, whose exact shape is reverse-engineered from the protocol description, through a stochastic subgradient method in which the link updates its persistence probability based on its transmission success or failure. We prove that existence of a Nash equilibrium is guaranteed in general. Then we establish the minimum amount of backoff aggressiveness needed, as a function of density of active users, for uniqueness of Nash equilibrium and convergence of the best response strategy. Convergence properties and connection with the best response strategy are also proved for variants of the stochastic-subgradient-based dynamics of the game. Together with known results in reverse-engineering TCP and BGP, this paper further advances the recent efforts in reverse-engineering layers 2-4 protocols. In contrast to the TCP reverse-engineering results in earlier literature, MAC reverse-engineering highlights the non-cooperative nature of random access.