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We analyze a family of solution procedures for games with incomplete information that do not require the specification of an epistemic type spaceà la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions ∆ on first-order beliefs. For any fixed ∆ we obtain a solution called strong ∆-rationalizability. In static games, strong ∆-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibriumdoi:10.2202/1534-5963.1073 fatcat:vzfjvbqiljh63b7l4al432jvwu