Partial Identification Under Iterated Strict Dominance

Abstract

I use an Iterated Strict Dominance (ISD) argument to build bounds on the distribution of outcomes of games and use them to pin down an identified set for the parameters of interest. These bounds (ISD Bounds) are robust to equilibrium multiplicity, pure and mixed, and to any non-equilibrium play as long as it is consistent with ISD. Furthermore, ISD Bounds apply to games of complete or incomplete information, with discrete or continuous actions of any dimensionality, as well as games with unobserved heterogeneity. To maximize the “bite” of the ISD Bounds, I introduce Strategically Monotonic Supermodular Games, i.e., games of strategic complements/substitutes where players’ payoffs are supermodular in their actions. I show that ISD rules out large swaths of the strategy set for this type of game via an easy-to-compute sequence of best-response iterations. Moreover, I show that for binary games the resulting identified set is sharp. Finally, I apply ISD Bounds to an entry game for the airline industry and use the estimates to evaluate the impact of the proposed merger between JetBlue and Spirit. This exercise proves that ISD Bounds are informative about the parameters of interest in practical applications.