Introduction
Repeated games are a type of game that are usually modeled in game theory. The term “repeated game” refers to a game that is repeated over a period of time, with each repetition playing a role in the overall outcome of the game. A repeated game can be anything from a simple game of tic-tac-toe being played by a pair of children to a complex game of chess with tens of thousands of moves being considered. The most common form of game theory modeling of a repeated game is one in which the players have perfect recall, meaning they remember all the moves of the past and can base their play on those past moves.
Theoretical Background
Modeling repeated games requires an understanding of two main concepts: strategies and equilibrium. A strategy is an action that a player takes in the hopes of maximizing their reward or minimizing losses, depending on their role in the game. An equilibrium describes the state in which all players are making the best choice for themselves given all players’ current strategies.
Different Models of Repeated Game Play
There are several different models for repeated game play that can be used to model different types of games. The two main models are the finitely repeated and infinitely repeated games. In a finitely repeated game, the game is repeated a fixed number of times. This model has been used to analyze games with perfect information, where all players are aware of their opponents’ moves. This model has also been used to analyze games with imperfect information, where the players do not have perfect knowledge of their opponents’ moves.
Another model is the infinitely repeated game. This is a game that is repeated an infinite number of times. This model has been used to analyze games with perfect information, as well as games with imperfect information. The infinite repetition of a game is useful in situations where an infinite number of moves must be considered. In an infinitely repeated game, a player must take into account all of the possible future moves of their opponents in order to make the most profitable decision for themselves.
Rationality and Punishment
In a repeated game, the players must often act rationally in order to maximize their returns from the game. The rational outcome of a game is usually different from the outcome that would be expected from a single game, as the players must also consider the returns from future games. Rational decision-making can be modeled using the concept of punishment. Punishment is the idea that by punishing an opponent’s actions in the current round of the game, a player can discourage the opponent from taking advantage of them in future rounds.
Conclusion
Repeated games are a popular topic of study in the field of game theory. By using the concepts of strategies, equilibrium, and punishment, game theorists have been able to model different types of repeated games. Finitely repeated games serve as an analysis of games with either perfect or imperfect information, while infinitely repeated games are a useful tool for analyzing games with an infinite number of possible moves. By examining the actions of players in repeated games, as well as the strategies for maximizing rewards and minimizing losses, game theorists can better understand how decision-making is affected by circumstances, strategies, and external events.
