<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-deformed evolutionary dynamics in simple matrix games

We consider evolutionary games in which the agent selected for update compares strategies with q neighbors, rather than a single neighbor as in standard evolutionary game theory. If all q sampled neighbors agree, then agents update their strategy using a smoothed best-response rule. Following ideas from social impact theory, we also study mathematical generalizations of the dynamics to noninteger q>0. Looking at fixed point stability and fixation times for 2×2 games with all-to-all interactions, we find that the flow changes significantly as a function of q. Further, we develop the pair approximation for the q-deformed dynamics on uncorrelated graphs. We also study 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 within the simplex.