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 a 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 a temperature increase on the underlying system and identify surprising properties of this model through numerical simulations.
Original language | English (US) |
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Article number | 103103 |
Journal | Chaos |
Volume | 32 |
Issue number | 10 |
DOIs | |
State | Published - Oct 1 2022 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics