Aloha Games with Spatial Reuse

Aloha games study the transmission probabilities of a group of non-cooperative users which share a channel to transmit via the slotted Aloha protocol. This paper extends the Aloha games to spatial reuse scenarios, and studies the system equilibrium and performance. Specifically, fixed point theory and order theory are used to prove the existence of a least fixed point as the unique Nash equilibrium (NE) of the game and the optimal choice of all players. The Krasovskii's method is used to construct a Lyapunov function and obtain the conditions to examine the stability of the NE. Simulations show that the theories derived are applicable to large-scale distributed systems of complicated network topologies. An empirical relationship between the network connectivity and the achievable total throughput is finally obtained through simulations.