Economics Game Theory Questions Long
In game theory, repeated games refer to a class of games where the same strategic interaction is played repeatedly over a period of time. Unlike one-shot games, where players make decisions without considering the future consequences, repeated games allow players to take into account the impact of their actions on future rounds of the game.
The concept of repeated games is based on the assumption that players are rational and forward-looking, aiming to maximize their long-term payoffs. By playing the game multiple times, players have the opportunity to learn from past experiences, develop strategies, and adjust their behavior accordingly.
There are two main types of repeated games: finitely repeated games and infinitely repeated games.
1. Finitely Repeated Games:
In finitely repeated games, the number of rounds is predetermined and known to all players. Each round is treated as a one-shot game, and players make decisions based on their short-term interests. However, since players are aware of the limited number of rounds, they may consider the potential consequences of their actions on future rounds. This introduces a strategic element into the decision-making process.
Finitely repeated games can be analyzed using backward induction, a technique that starts from the last round and works backward to determine the optimal strategy for each player at each stage. This analysis helps identify subgame perfect equilibria, which are strategies that are optimal not only in the current round but also in all subsequent rounds.
2. Infinitely Repeated Games:
In infinitely repeated games, the number of rounds is not predetermined and the game continues indefinitely. This allows for more complex strategies and the possibility of cooperation between players. Players can establish reputations, build trust, and enforce agreements over time.
In infinitely repeated games, players can adopt various strategies, such as tit-for-tat, trigger strategies, or grim trigger strategies. Tit-for-tat is a simple strategy where a player initially cooperates and then mimics the opponent's previous move in each subsequent round. Trigger strategies involve punishing the opponent for deviating from cooperation, while grim trigger strategies involve permanently punishing the opponent for any deviation.
The analysis of infinitely repeated games often involves the concept of discounting, which assigns less weight to future payoffs compared to immediate payoffs. This reflects the fact that players value immediate gains more than uncertain future gains. By discounting future payoffs, players can determine the optimal strategy that balances short-term gains with the potential benefits of cooperation in the long run.
Overall, repeated games provide a framework for studying strategic interactions over time. They allow for the analysis of cooperative behavior, the emergence of trust and reputation, and the impact of past actions on future outcomes. By considering the dynamics of repeated interactions, game theory provides insights into real-world situations where individuals or firms engage in repeated decision-making processes.