Article Outline
Glossary
Definition of the Subject
Introduction
A Canonical Model
Two Long‐Lived Players
Future Directions
Acknowledgments
Bibliography
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Abbreviations
- Action type:
-
A type of player who is committed to playing a particular action, also called a commitment type or behavioral type.
- Complete information:
-
Characteristics of all players are common knowledge.
- Flow payoff:
-
Stage game payoff.
- Imperfect monitoring:
-
Past actions of all players are not public information.
- Incomplete information:
-
Characteristics of some player are not common knowledge.
- Long-lived player:
-
Player subject to intertemporal incentives, typically has the same horizon as length of the game.
- Myopic optimum:
-
An action maximizing stage game payoffs.
- Nash equilibrium:
-
A strategy profile from which no player has a profitable unilateral deviation (i. e., it is self‐enforcing).
- Nash reversion:
-
In a repeated game, permanent play of a stage game Nash equilibrium.
- Normalized discounted value:
-
The discounted sum of an infinite sequence \( { \{a_t\}_{t\ge 0} } \), calculated as \((1-\delta)\sum_{t\ge 0}\delta^ta_t \), where \( { \delta\in (0,1) } \) is the discount value.
- Perfect monitoring:
-
Past actions of all players are public information.
- Repeated game:
-
The finite or infinite repetition of a stage game.
- Reputation bound:
-
The lower bound on equilibrium payoffs of a player that the other player(s) believe may be a simple action type (typically the Stackelberg type).
- Short-lived player:
-
Player not subject to intertemporal incentives, having a one‐period horizon and so is myopically optimizing.
- Simple action type:
-
An action who plays the same (pure or mixed) stage-game action in every period, regardless of history.
- Stage game:
-
A game played in one period.
- Stackelberg action:
-
In a stage game, the action a player would commit to, if that player had the chance to do so, i. e., the optimal commitment action.
- Stackelberg type:
-
A simple action type that plays the Stackelberg action.
- Subgame:
-
In a repeated game with perfect monitoring, the game following any history.
- Subgame perfect equilibrium:
-
A strategy profile that induces a Nash equilibrium on every subgame of the original game.
- Type:
-
The characteristic of a player that is not common knowledge.
Bibliography
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Acknowledgments
I thank Eduardo Faingold, KyungMin Kim, Antonio Penta, and Larry Samuelson for helpful comments.
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Mailath, G.J. (2012). Reputation Effects. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_163
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