Cooperation and free riding with moral cost
Résumé
We study social organizations with
possible coexistence at equilibrium of
cooperating individuals and pure consumers
(free-riders). We investigate this polymorphic
equilibrium using a game-theoretic approach and
a statistical physics analysis of a simple model.
The agents face a binary decision problem:
whether to contribute or not to the public good,
through the maximization of an additive utility
that has two competing terms, a fixed cost for
cooperating and an idiosyncratic moral cost for
free-riding proportional to the fraction of
cooperators. We study the equilibria regimes of
this model. We show that there is a fraction of
expected cooperators below which cooperation
fails to emerge. Besides the homogeneous stable
equilibria (everybody cooperates or everybody
free-rides), it exists a solution in which
cooperators coexist with free-riders. This
polymorphic equilibrium is a consequence of the
heterogeneous (idiosyncratic) perceptions of the
social reproval by the different individuals. We
provide analytic results in the case of a simple
distribution of the idiosyncratic moral weights,
and discuss them on the basis of concepts of
game theory.
possible coexistence at equilibrium of
cooperating individuals and pure consumers
(free-riders). We investigate this polymorphic
equilibrium using a game-theoretic approach and
a statistical physics analysis of a simple model.
The agents face a binary decision problem:
whether to contribute or not to the public good,
through the maximization of an additive utility
that has two competing terms, a fixed cost for
cooperating and an idiosyncratic moral cost for
free-riding proportional to the fraction of
cooperators. We study the equilibria regimes of
this model. We show that there is a fraction of
expected cooperators below which cooperation
fails to emerge. Besides the homogeneous stable
equilibria (everybody cooperates or everybody
free-rides), it exists a solution in which
cooperators coexist with free-riders. This
polymorphic equilibrium is a consequence of the
heterogeneous (idiosyncratic) perceptions of the
social reproval by the different individuals. We
provide analytic results in the case of a simple
distribution of the idiosyncratic moral weights,
and discuss them on the basis of concepts of
game theory.