Introduction to Repeated Games in Game Theory
The Grim Trigger Strategy is a prominent strategy used in repeated games. It is a form of retaliation where a player will continue to punish the other player for any deviation from cooperation. The punishment is severe and continues indefinitely, leading to a situation where both players end up with a lower payoff. This strategy is also known as 'Tit for Tat with Forgiveness'.
The Grim Trigger Strategy is based on the concept of trigger strategies. A trigger strategy is a set of instructions that a player follows when the other player deviates from the cooperative path. The Grim Trigger Strategy is a particular form of a trigger strategy, where the punishment is severe and continues indefinitely.
The Grim Trigger Strategy is often used in the context of the Prisoner's Dilemma game, where two players have to choose between cooperation and defection. If both players cooperate, they both receive a high payoff. If one player defects while the other cooperates, the defector receives a higher payoff while the cooperator receives a lower payoff. If both players defect, they both receive a low payoff. In this game, the Grim Trigger Strategy can be used to enforce cooperation between the players.
For example, if Player A and Player B are playing the Prisoner's Dilemma game using the Grim Trigger Strategy, and Player B defects in one round, Player A will punish Player B by defecting in all subsequent rounds. This punishment will continue indefinitely, leading to a situation where both players receive a lower payoff.
The Grim Trigger Strategy is a powerful tool in repeated games, as it can enforce cooperation even in situations where defection is the dominant strategy. However, it is important to note that the strategy is only effective in situations where the players have a long-term relationship and expect to interact with each other multiple times. In situations where the players only interact once, the Grim Trigger Strategy loses its effectiveness.
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