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A common observation in the informal literature of economics (and elsewhere) is that in multistage "games," players may seek early in the game to acquire a reputation for being "tough" or "benevolent" or something else. But this phenomenon is not observed in some formal game-theoretic analyses of finite games, such as Selten's finitely repeated chain-store game or in the finitely repeated prisoners' dilemma. We reexamine Selten's model, adding to it a "small" amount of imperfect (or incomplete) information about players' payoffs, and we find that this addition is sufficient to give rise to the "reputation effect" that one intuitively expects. Journal of Economic Literature,

A common observation in experiments involving finite repetition of the prisoners' dilemma is that players do not always play the single-period dominant strategies ("finking"), but instead achieve some measure of cooperation. Yet finking at each stage is the only Nash equilibrium in the finitely repeated game. We show here how incomplete information about one or both players' options, motivation or behavior can explain the observed cooperation. Specifically, we provide a bound on the number of rounds at which Fink may be played, when one player may possibly be committed to a "Tit-for-Tat" strategy.