Participation incentives on a wireless random access erasure collision channel

Random medium access on wireless channels has two key characteristics: heterogeneous channel quality across users (due to the variable wireless channel conditions with the access point across users) and packet collisions (due to random access) at the access point. The design of optimal channel contention probabilities is nontrivial on account of the need to balance between under-utilization (no transmission attempts) and over-utilization (channel collisions) of the wireless channel. The wireless random access erasure collision channel presented in this paper is a parsimonious abstraction of these phenomena. We consider a scenario wherein the base station provides a reward to users in proportion to the rate of successfully received packets, and users incur a cost in proportion to their contention probability. The objective is to select a reward such that the sum-user delivered rate in the equilibrium of the induced game is (approximately) optimal, i.e., such that only higher quality users are incentivized to contend the channel. We use the price of anarchy (PoA) measure and study the extent to which appropriate reward mechanisms can yield good PoA bounds.