"Efficient
Social Contracts and Population Growth"
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Abstract:
Social contracts are sets of conventions that allow members of human or
non-human societies to coordinate their actions. Those conventions
might be more or less efficient, where efficiency means absence of
waste. Standard evolutionary game theoretic models, such as the
replicator dynamics, do not offer good explanations of the evolution of
cooperative behavior in games where there is an efficient but risky,
and a less risky but inefficient equilibrium. A simple game of this
kind is the Stag Hunt game. We will investigate the evolution of
cooperative behavior in the Stag Hunt game in finite populations with
the potential to grow. In order to do this, we employ a stochastic
model which is connected to the replicator dynamics by some limiting
results. However, due to the higher growth rate of cooperative
individuals and due to drift phenomena that can occur while the
population is small, in the stochastic model an efficient population of
cooperators is more likely to emerge from a not entirely cooperating
initial population than in the replicator dynamics. By introducing
environmental pressure we find even more cooperating societies among
the populations that do not go extinct during the initial periods of
play.