Pairwise Comparison Evolutionary Dynamics With Strategy-Dependent Revision Rates: Stability and $\delta$-Passivity

Abstract

We report on new sufficient conditions for the stability of evolutionary dynamics in population games. A large number of agents interact noncooperatively in a population game by selecting strategies based on their payoffs. Each agent is allowed to revise its strategy repeatedly with an average frequency referred to as the revision rate. We are interested in the case where an agent's current strategy influences directly the revision rate. Existing stability results for this case assume that a memoryless potential game generates the strategies' payoffs. This article extends these results to allow for payoff mechanisms that can be either dynamic or memoryless games that do not have to be potential. To make our analysis concrete, we assume that the agents' revision preferences follow a so-called pairwise comparison protocol. These protocols are ubiquitous because they operate fully decentralized and with minimal information requirements (they need to access only the payoff values, not the mechanism). We use a well-motivated example to illustrate an application of our framework.