  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.
