A game theoretical approach for transmission strategies in slotted ALOHA networks with multi-packet reception

In this paper we consider finite-size slotted ALOHA sensor networks with multiple packet reception capability and selfish sensors. Each sensor wishes to maximize its individual expected reward. We exploit decentralized channel state information (CSI) to obtain transmission policies that are optimal for each sensor The problem is formulated as a finite player finite action, non-cooperative stochastic game where each sensor is a selfish but rational player We prove for the first time that under the signal to interference noise ratio (SINR) threshold reception model the optimal transmission policy for each player belongs to the class of threshold policies. As a result, there exists a Nash equilibrium at which all players adopt pure strategies. The optimality of threshold policies greatly simplifies the estimation of optimal transmission schemes. We present a provably convergent algorithm for finding the threshold for each sensor and illustrate its performance via numerical examples.