Research

Is there any difference in how I believe my opponents reason about my rationality as opposed to the rationality of others? To address this question, we introduce introspection into the ring games (Kneeland, 2015). In these games, one player makes multiple decisions, forcing her to reason about how others reason about her rationality. We assess experimentally whether the presence of introspection modifies the orders of revealed-rationality compared to ring games without introspection. Although epistemic game theory does not distinguish between these scenarios, our findings reveal that introspection indeed has an effect on subjects’ revealed orders of rationality. Specifically, introspection increases the order of revealed-rationality among less rational players in the classic ring games, while it decreases the order of revealed-rationality among more rational players.

• Submitted. Available at SSRN.

We use the direct-sum decomposition proposed by Candogan et al. (2011) to decompose any finite game into the strategic and the nonstrategic components. Nash equilibrium is invariant to changes in the nonstrategic component. Mutual-Max-Sum, a new solution concept, depends only on the nonstrategic component. We design 3x3 games to empirically test, whether and when, manipulations in the nonstrategic component affect individual behavior and whether Mutual-Max-Sum is behaviorally relevant. We find that manipulations of the nonstrategic component significantly affect individual behavior and that Mutual-Max-Sum is able to attract individual behavior mostly when it is also payoff dominant.

• Submitted. Available here.

Dynamic refinements of game-theoretic solution concepts are designed to leverage the temporal structure of games. But to what extent are these concepts robust to the relaxation of common belief in rationality? Using a dynamic p-belief operator–where people believe in an event with probability at least p and which imposes conditional probabilities whenever possible–we establish a theoretical equivalence between static rationalizability and dynamic p-rationalizability, regardless how dynamic rationality is defined. We also show that the set of weak sequential equilibria coincides with the set of profiles that are approximate p-equilibria, a relaxation of subgame perfect equilibria, for any p< 1. Notably, the dynamic solution concepts do not converge to their classic counterparts as p → 1. This implies that even the slightest doubt about others’ rationality renders dynamic reasoning essentially static. These results help explaining cooperation in finitely repeated Prisoner’s Dilemma and Centipede games, and the empirical failure of backward and forward induction in various settings.

• Last version available here.