"The impact of time delay on mutant fixation in evolutionary games"Mohamadichamgavi, JavadEvolutionary game theory provides a powerful framework for understanding how strategies spread and persist in populations through replication and imitation based on fitness. Traditional models have assumed instantaneous dynamics where an individual's fitness is determined solely by the current population state. However, many biological and social processes involve time delays, where outcomes depend on events in the past rather than just the present state. This motivates incorporating time delays into evolutionary game theory models, such that an individual's fitness is determined by the population composition at some previous time point. We investigate the effects of time delays on the fixation dynamics of mutations in finite populations following a Moran Birth-death process with two strategies. We model this as an absorbing Markov chain and derive analytical expressions for the fixation probability and time as a function of the time delay. We apply this analysis to three different game types: the Stag-Hunt game, the Snowdrift game, and the Prisoner's Dilemma game. Our results reveal that time delays can significantly impact fixation dynamics in an intricate way that depends on the underlying game payoffs. In the Stag-Hunt game, increasing time delays reduces the fixation probability of a new mutation. Conversely, in the Snowdrift game, longer time delays enhance the fixation probability. For the Prisoner's Dilemma, time delays decrease fixation for both cooperative and defective initial mutation. Time delays also affect the fixation time across the different games. These findings highlight the importance of considering time delays when modeling evolutionary processes, as neglecting such delays can miss crucial aspects of the underlying dynamics. |
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