"Kindergarten Model: Approximating Time Delays in Evolutionary Games"Fic, MałgorzataReal-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems and leads to models that are challenging to analyse and computationally expensive to solve. In this work, we propose an intermediate solution to resolve the issue in the framework of evolutionary game theory. Our compartment-based approximation model includes time delays while remaining relatively simple and straightforward to analyse. We show that the approximation yields qualitatively comparable results with models considering explicit delays. Particularly, we focus on the case of delays between parents' interaction and an offspring joining the population, with the magnitude of the delay depending on the parents' strategy. We analyse the stag-hunt game, the snowdrift game and the prisoner's dilemma and show that strategy-dependent delays are detrimental to affected strategies. Additionally, we present how including delays may change the effective games played in the population, subsequently emphasising the importance of considering the studied systems' temporal aspects to model them accurately. |
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