We introduce a class of evolutionary game dynamics — <em>pairwise comparison dynamics</em> — under which revising agents choose a candidate strategy at random, switching to it with positive probability if and only if its payoff is higher than the agent’s current strategy. We prove that all such...

We consider a model of evolution in games in which a revising agent observes the actions of a random number of randomly sampled opponents and then chooses a best response to the distribution of actions in the sample. We provide a condition on the distribution of sample sizes under which an...

Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols....

We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. We also show that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics....

We consider a discrete choice model in which the payoffs to each of an agentʼs n actions are subjected to the average of m i.i.d. shocks, and use tools from large deviations theory to characterize the rate of decay of the probability of choosing a given suboptimal action as m approaches...

We consider a model of stochastic evolution under general noisy best response protocols, allowing the probabilities of suboptimal choices to depend on their payoff consequences. Our analysis focuses on behavior in the small noise double limit: we first take the noise level in agents' decisions...

We consider models of stochastic evolution in two-strategy games in which agents employ imitative decision rules. We introduce committed agents: for each strategy, we suppose that there is at least one agent who plays that strategy without fail. We show that unlike the standard imitative model,...

A population of agents recurrently plays a two-strategy population game. When an agent receives a revision opportunity, he chooses a new strategy using a noisy best response rule that satisfies mild regularity conditions; best response with mutations, logit choice, and probit choice are all...

We prove that any regular ESS is asymptotically stable under any impartial pairwise comparison dynamic, including the Smith dynamic; under any separable excess payoff dynamic, including the BNN dynamic; and under the best response dynamic. Combined with existing results for imitative dynamics, our...

We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. We also show that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics....