Obey or play: asymptotic equivalence of slotted Aloha with a game theoretic contention model

Contention control is an important means to mitigate adverse affects of multiple access interference on transmitted data packets in wireless communication networks. Most practical contention control mechanisms, e.g., IEEE 802.11 and slotted Aloha, rely on the assumption that all users abide with the rules of the protocol. There is also a growing body of work employing game theoretic techniques to gain new design insights for controlling contention when users act selfishly to maximize their perceived performance, as well as to reverse/forward engineer existing contention control protocols. In this paper, it is shown that the asymptotic behaviour of the slotted Aloha protocol when the number of contenders grows large coincides with a Nash equilibrium that is derived from a game theoretic contention model. Furthermore, the relationship between the design parameters in both approaches is established. In particular, it is shown that the back-off exponent in the slotted Aloha based contention control is linearly related to the cost of a collision in the game theoretic approach.