Evolutionary Dynamics of the Nash Demand Game: A Diffusion Approach

Cooperation is fundamental in animal societies including humans, yet how to divide the resources obtained through cooperation is not a trivial question. The Nash demand game provides an excellent framework to study resource division between selfish agents. We herein study evolutionary dynamics of strategies in the Nash demand game. Our evolutionary model confirms the traditional prediction based on a Nash-equilibrium analysis that any possible resource division can be a stable outcome. Next, we study the effect of mutation (or exploration in cultural evolution). We model mutation as diffusion in the strategy space and analyze a pair of reaction diffusion equations. We find that the introduction of mutation to the system dramatically alters evolutionary outcomes and leads to a fair split of resources between two agents. We also study the effect of asymmetry in selection intensity on the resulting pattern of resource division.