In a repeated game, how does the outcome differ if firms...

In a repeated game, how does the outcome differ if firms know that the game will be (a) repeated indefinitely, (b) repeated a known, finite number of times, and (c) repeated a finite number of times but the firms are always unsure whether the current period will be the last? (Hint: See Solved Problem $14.2 .$

Key Concepts

Backward Induction

This is a method used to solve finite games by analyzing them from the end of the game backward to the beginning. In finitely repeated games, backward induction helps explain why cooperation may break down as players deduce that defection in the last period is inevitable, which then unravels cooperation in earlier periods.

Finite Repetition

In a finitely repeated game with a known endpoint, players can calculate future actions by backward induction. This typically leads to a unraveling of cooperative behavior, as players anticipate that non-cooperative behavior is optimal in the final period. As a result, the equilibrium outcome is often non-cooperative, even if a cooperative outcome might be beneficial if the game were to continue indefinitely.

Uncertainty about the Terminal Period

When players are unsure whether the current period is the last, the strategic horizon effectively becomes indefinite. This uncertainty can reinforce cooperative behavior because the possibility of the game continuing discourages myopic defection. The lack of a clear endpoint mitigates the endgame effect, thereby sustaining mutually beneficial strategies even in a framework where the number of repetitions is finite.

Repeated Games

This concept refers to strategic interactions that occur repeatedly over time, allowing players to condition their strategies on past behavior. The history of play influences future actions, facilitating outcomes that differ significantly from those in one-shot games. Repeated games provide a framework to analyze how cooperation or punishment can be sustained over time through mechanisms like reputation and reciprocal actions.

Infinite Repetition (Indefinite Horizon)

When a game is repeated indefinitely, players face no predetermined end, which allows for the enforcement of cooperative strategies through the threat of future punishment for deviation. This environment makes a wide range of equilibrium outcomes possible, as described by the Folk Theorem, since the long-term consequences of current actions can outweigh short-term gains from defection.

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