Risk Dominance - Equilibrium Selection

Equilibrium Selection

A number of evolutionary approaches have established that when played in a large population, players might fail to play the payoff dominant equilibrium strategy and instead end up in the payoff dominated, risk dominant equilibrium. Two separate evolutionary models both support the idea that the risk dominant equilibrium is more likely to occur. The first model, based on replicator dynamics, predicts that a population is more likely to adopt the risk dominant equilibrium than the payoff dominant equilibrium. The second model, based on best response strategy revision and mutation, predicts that the risk dominant state is the only stochastically stable equilibrium. Both models assume that multiple two-player games are played in a population of N players. The players are matched randomly with opponents, with each player having equal likelihoods of drawing any of the N−1 other players. The players start with a pure strategy, G or H, and play this strategy against their opponent. In replicator dynamics, the population game is repeated in sequential generations where subpopulations change based on the success of their chosen stratregies. In best response, players update their strategies to improve expected payoffs in the subsequent generations. The recognition of Kandori, Mailath & Rob (1993) and Young (1993) was that if the rule to update one's strategy allows for mutation4, and the probability of mutation vanishes, i.e. asymptotically reaches zero over time, the likelihood that the risk dominant equilibrium is reached goes to one, even if it is payoff dominated.3