Abstract below

Andrew Belmonte

William G. Pritchard Laboratory for Experiments and Applied Mathematics
Pennsylvania State University

New patterns of cooperation in evolutionary games

The equations of evolutionary game theory represent different fundamental aspects of the underlying biological or social system, and by expanding these appropriately we may uncover new phenomena. In the Prisoner’s Dilemma game, spatial extension is known to allow for the coexistence of Cooperation with the dominant Defect strategy, typically as intricate and nonstationary patterns. We numerically study a modified evolutionary game in which players store the sum of all previous winnings in a cache or bank, similar to stored body fat or other carryover effects in ecology; players imitate others with a higher stored value. This results in stationary patterns of coexistence, moreover a single cooperator, endowed with a sufficient stored value, can nucleate a pattern of coexistence among defectors. In another study, we investigate the Rock-Paper-Scissors game using a similar approach, and find conditions for the formation of stable communities. The imposition of thermal randomness via a Boltzmann distribution leads to the progressive melting of the patterns.

This is joint work with Alex Galvin, Connor Olson, and Christopher Griffin.