q-deformed evolutionary dynamics in simple matrix games

TL;DR

This paper introduces a q-deformed evolutionary game framework where agents compare payoffs to multiple neighbors, revealing significant changes in dynamics and flow patterns across different game topologies and strategies.

Contribution

It develops a novel q-deformed model for evolutionary games, analyzing stability, fixation times, and flow changes in various network structures and multi-strategy scenarios.

Findings

Flow dynamics vary significantly with q

Changing topology affects evolutionary outcomes

New flow patterns emerge in multi-strategy games

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.