The Impact of Time Delay on Mutant Fixation in Evolutionary Games
arxiv(2024)
摘要
Evolutionary game theory examines how strategies spread and persist in
populations through reproduction and imitation based on their fitness.
Traditionally, models assume instantaneous dynamics where fitness depends on
the current population state. However, some real-world processes unfold over
time, with outcomes emerging from history. This motivates incorporating time
delays into evolutionary game models, where fitness relies on the past. We
study the impact of time delays on mutant fixation in a Moran Birth-death
process with two strategies in a well-mixed population. At each time step of
the process, an individual reproduces proportionally to fitness coming from the
past. We model this as an absorbing Markov chain, allowing computational
calculation of the fixation probability and time. We focus on three important
games: the Stag-Hunt, Snowdrift, and Prisoner's Dilemma. We will show time
delays reduce the fixation probability in the Stag-Hunt and the Prisoner's
Dilemma but increase it in the Snowdrift. For the Stag-Hunt and the Prisoner's
Dilemma, time delays lengthen the fixation time until a critical point, then
reduce it. The Snowdrift exhibits the opposite trend.
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