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arXiv · 2206.13160

Community Formation in Wealth-Mediated Thermodynamic Strategy Evolution

Connor Olson·Andrew Belmonte·Christopher Griffin
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Abstract

We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale which defines the random fluctuations. Players with higher bank values are thus less likely to change strategy than players with lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of temperature increase on the underlying system, and identify surprising properties of this model through numerical simulations.

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Connor Olson, Andrew Belmonte, Christopher Griffin. 2022-06-27. Community Formation in Wealth-Mediated Thermodynamic Strategy Evolution. https://doi.org/10.1063/5.0105969

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