Communities form when accumulated wealth is used as a proxy for success

What is it about?

When we think about a "game" we usually think about whether we win or lose in that game. But in life we accumulate wins and losses over time. In this paper we ask the question: if players are arranged on a grid and play rock-paper-scissors with their neighbors what happens when accumulated winnings are used to influence future strategy choice? In our model, communities of "rocks" "papers" and "scissors" form and how those communities evolve is strongly influenced by the relative reward for winning vs. losing and the tendency of players to randomly switch strategies.

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Photo by Jonathan Petersson on Unsplash

Photo by Jonathan Petersson on Unsplash

Why is it important?

Traditional Darwinian evolution asserts that natural selection is driven by competition and mutation repeated over deep time, producing species mutually adapted to their environments and each other. Evolutionary game theory represents this process via (e.g.) the replicator or replicator-mutator equation, considering instantaneous reward from interaction as the measure of fitness. This approach, however, neglects the ability of organisms to store energy thereby insulating themselves from negative interactions. That is, fitness is (in some sense) measured by overall historical success as well as instantaneous success. In this paper, we study a spatial evolutionary game mechanism that incorporates mutation via a Boltzmann distribution but is mediated by stored (gross) winnings, or wealth. We derive conditions where communities form with high probability and study the resulting community structures theoretically and empirically in one dimension.

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