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This paper uses a laboratory experiment to study beliefs and their relationship to action and strategy choices in finitely and indefinitely repeated prisoners' dilemma games. We find subjects' elicited beliefs about the other player's action are generally accurate despite some systematic deviations, and anticipate the evolution of behavior differently between the finite and indefinite games. We also use the elicited beliefs over actions to recover beliefs over supergame strategies played by the other player. We find these beliefs over strategies correctly capture the different classes of strategies played in each game, vary substantially across subjects, and rationalize their strategies.
