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We report on new stability conditions for evolutionary dynamics in the context of population games. We adhere to the prevailing framework consisting of many agents, grouped into populations, that interact noncooperatively by selecting strategies with a favorable payoff. Each agent is repeatedly allowed to revise its strategy at a rate referred to as revision rate. Previous stability results considered either that the payoff mechanism was a memoryless potential game, or allowed for dynamics (in the payoff mechanism) at the expense of precluding any explicit dependence of the agents revision rates on their current strategies. Allowing the dependence of revision rates on strategies is relevant because the agents strategies at any point in time are generally unequal. To allow for strategy-dependent revision rates and payoff mechanisms that are dynamic (or memoryless games that are not potential), we focus on an evolutionary dynamics class obtained from a straightforward modification of one that stems from the so-called impartial pairwise comparison strategy revision protocol. Revision protocols consistent with the modified class retain from those in the original one the advantage that the agents operate in a fully decentralized manner and with minimal information requirements - they need to access only the payoff values (not the mechanism) of the available strategies. Our main results determine conditions under which system-theoretic passivity properties are assured, which we leverage for stability analysis.
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. W
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evoluti
In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different environmen
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player an
After Laskar, the Lyapunov time in the solar system is about five millions years (5.000.000 [years]). On the other hand, after Kimura, the evolutionary (phenotypic) rate, for hominids, is 1/5.000.000 [1/years]. Why are these two quantities so closely