Ex-post regret heuristics under private values (I): Fixed and random matching

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In contexts in which players have no priors, we analyze a heuristic process based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are randomly matched to play the game (random matching). The relevant long run predictions are minimal sets that are “closed under same or better reply” operations. Under additional assumptions in each case, the predictions boil down to Nash equilibria, ex-post equilibria or minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in several applications, including second-price auctions, first-price auctions and Bertrand duopolies.