Stochastic Congestion Games with Risk-Averse Players

Congestion games ignore the stochastic nature of resource delays and the risk-averse attitude of the players to uncertainty. To take these aspects into account, we introduce two variants of atomic congestion games, one with stochastic players, where each player assigns load to her strategy independently with a given probability, and another with stochastic edges, where the latency functions are random. In both variants, the players are risk-averse, and their individual cost is a player-specific quantile of their delay distribution. We focus on parallel-link networks and investigate how the main properties of such games depend on the risk attitude and on the participation probabilities of the players. In a nutshell, we prove that stochastic congestion games on parallel-links admit an efficiently computable pure Nash equilibrium if the players have either the same risk attitude or the same participation probabilities, and also admit a potential function if the players have the same risk attitude. On the negative side, we present examples of stochastic games with players of different risk attitudes that do not admit a potential function. As for the inefficiency of equilibria, for parallel-link networks with linear delays, we prove that the Price of Anarchy is Θ(n), where n is the number of stochastic players, and may be unbounded, in case of stochastic edges.