When to arrive in a congested system: Achieving equilibrium via learning algorithm

Motivated by applications in competitive WiFi sensing, and competition to grab user attention in social networks, the problem of when to arrive at/sample a shared resource/server platform with multiple players is considered. Server activity is intermittent, with the server switching between ON and OFF periods alternatively. Each player spends a certain cost to sample the server state, and the per-player payoff is inversely proportional to the number of simultaneously connected/arrived players. The objective of each player is to arrive/sample the server as soon as any ON period begins while incurring minimal sensing cost and to avoid having many other players overlap in time with itself. For this competition model, we propose a distributed randomized learning algorithm (strategy to sample the server) for each player, which is shown to converge to a unique non-trivial fixed point. The fixed point is moreover shown to be a Nash equilibrium of a game, where each player's utility function is demonstrated to possess all the required selfish tradeoffs.