On equilibrium refinement in supermodular games - Oriol Carbonell-Nicolau; Richard P. McLean (Rutgers University, Department of Economics, 2012)
We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategies. We illustrate that, in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We prove that when the set of undominated actions is a sublattice, supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria that can be obtained as limits of undominated actions.
Keywords: C72; 330; supermodular game; weakly dominated strategy; trembling-hand perfect equilibrium; strategically stable set; supermodular game; weakly dominated strategy; trembling-hand perfect equilibrium; strategically stable set