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arXiv · 2407.16380

q-deformed evolutionary dynamics in simple matrix games

Christopher R. Kitching·Tobias Galla
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Abstract

We consider evolutionary games in which the agent selected for update compares their payoff to q neighbours, rather than a single neighbour as in standard evolutionary game theory. Through studying fixed point stability and fixation times for 2x2 games with all-to-all interactions, we find that the flow changes significantly as a function of q. Further, we investigate the effects of changing the underlying topology from an all-to-all interacting system to an uncorrelated graph via the pair approximation. We also develop the framework for studying games with more than two strategies, such as the rock-paper-scissors game where we show that changing q leads to the emergence of new types of flow.

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Christopher R. Kitching, Tobias Galla. 2024-07-23. q-deformed evolutionary dynamics in simple matrix games. https://doi.org/10.1103/physreve.110.064319

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