On the Uniqueness of Nash Equilibrium in ALOHA Games with Group of Selfish Users

In a random access protocol a user controls its packet transmission according to the pre-defined backoff algorithm. Here, we consider an exponential backoff (EB) algorithm, which can be described by a three-tuple; i) the initial transmission probability, ii) the backoff factor, and iii) the number of stages. In this paper, we first formulate an ALOHA game which consists of two groups of honest and selfish users as a non-cooperative game. A honest user well behaves, whose packet transmission is subject to the EB algorithm, whereas a selfish user transmits its packet with equal probability all the time. Then, a partial proof is presented with respect to the unique existence of Nash equilibrium in the ALOHA game. The complete proof for the problem is still left open.