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The simplex game: can selfish users learn to operate efficiently in wireless networks?

We introduce and analyse the simplex game, a non--cooperative game between selfish heterogeneous players with bounded rationality that compete for limited resources. In this game, players are asked to place their bet among a set of B choices and the game rewards those in the minority. Players start out completely uneducated and naive but, through a selfish learning scheme that seeks to maximise their own gain, they become more experienced and quickly learn to adapt and perform with an unexpected efficiency. Employing methods of Statistical Physics (namely the theory of replicas) we establish explicit analytic estimates of the game's performance that clearly reflect the users' emergent efficiency. We further map the general simplex game to the minority game, a simple model introduced in the context of econophysics. This mapping allows us to study the effect that the number of choices has on the game's performance. For concreteness, our analysis has focused on a system of WLAN access points, but it can be customised to other networks with non-cooperative players, such as OFDMA.