Self-stabilizing Uncoupled Dynamics

Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player’s behavior is independent of the other players’ preferences. For uncoupled players, recognizing an equilibrium is a distributed computational task. Self-stabilizing uncoupled dynamics, then, capture both resilience to failure and distribution of knowledge. We initiate the study of these dynamics by analyzing their strength in a bounded-recall synchronous setting. We determine, for every size of game, the minimum number of periods of play that stochastic agents must recall in self-stabilizing uncoupled dynamics, and also in the special case when the game is guaranteed to have unique best replies. For deterministic agents, we give two self-stabilizing uncoupled protocols. One applies to all games and uses three steps of recall. The other uses two steps of recall and applies to games where each player has at least four available actions. We also prove that for uncoupled deterministic agents a single step of recall is insufficient to achieve self-stabilization, regardless of game size.