Coalitional stochastic stability

This paper takes the idea of coalitional behaviour groups of people occasionally acting together to their mutual benefit and incorporates it into the framework of evolutionary game theory that underpins the social learning literature. This paper defines an equilibrium selection criterion which we call coalitional stochastic stability (CSS). This differs from existing work on stochastic stability in that profitable coalitional deviations are given greater importance than unprofitable single player deviations. CSS states are characterized for all normal form games and this characterization is shown to give a lexicographic ranking of efficiency and risk-dominance for 2x2 games, although a further example demonstrates that efficient selection is not guaranteed in larger games despite the Pareto improving nature of the deviations underlying CSS. Successive examples illustrate how the model can be used to give theories of: (i) The persistence and direction of inegalitarian social norms; (ii) How collusive behaviour between firms can promote (as well as inhibit) price competition in Bertrand models; (iii) How one of the problems affecting stochastic stability methods large expected time to convergence to stable states can be mitigated using a coalitional approach, explaining how social change can occur in reasonable timescales and new technologies and standards can achieve rapid dominance, spending little time at heterogeneous steady states.