We show that in any game that is continuous at infinity, if a plan of action ai is played by a type ti in a Bayesian Nash equilibrium, then there are perturbations of ti for which ai is the only rationalizable plan and whose unique rationalizable belief regarding the play of the game is arbitrarily close to the equilibrium belief of ti. As an application to repeated games, we prove an unrefinable folk theorem: any individually rational and feasible payoff is the unique rationalizable payoff vector for some perturbed type profile. This is true even if perturbed types are restricted to believe that the repeated-game payoff structure and the discount factor are common knowledge.

We propose exact simulation-based procedures for: (i) testing mean-variance efficiency when the zero-beta rate is unknown, and (ii) building confidence intervals for the zero-beta rate. On observing that this parameter may be weakly identified, we propose LR-type statistics as well as heteroskedascity and autocorrelation corrected (HAC) Wald-type procedures, which are robust to weak identification and allow for non-Gaussian distributions including parametric GARCH structures. In particular, we propose confidence sets for the zero-beta rate based on "inverting" exact tests for this parameter; these sets provide a multivariate extension of Fieller's technique for inference on ratios. The exact distribution of LR-type statistics for testing efficiency is studied under both the null and the alternative hypotheses. The relevant nuisance parameter structure is established and finite-sample bound procedures are proposed, which extend and improve available Gaussianspecific bounds. Furthermore, we study the invariance to portfolio repacking property for tests and confidence sets proposed. The statistical properties of available and proposed methods are analyzed via aMonte Carlo study. Empirical results on NYSE returns show that exact confidence sets are very different from the asymptotic ones, and allowing for non-Gaussian distributions affects inference results. Simulation and empirical results suggest that LR-type statistics - with p-values corrected using the Maximized Monte Carlo test method - are generally preferable to their Wald-HAC counterparts from the viewpoints of size control and power.