Robust stochastic stability - Carlos Ferrer-Alós; Nick Netzer (University of Zurich, Department of Economics, 2012)
A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular N-player binary-action games. For the mistakes model, robust selection results obtain for best-reply dynamics in the same class of games under the weaker condition of strategic complementarity. Further, both the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation are robust.
Keywords: C72; D83; 330; learning in games; stochastic stability; radius-coradius theorems; logit-response dynamics; mutations; imitation; Stochastisches Spiel; Nichtkooperatives Spiel; Entscheidungstheorie