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If the iterated prisoner's dilemma is played a finite number of times and both players know this, then the dominant strategy and Nash equilibrium is to defect in all rounds. The proof is inductive : one might as well defect on the last turn, since the opponent will not have a chance to later retaliate.
Nash equilibrium requires that one's choices be consistent: no players wish to undo their decision given what the others are deciding. The concept has been used to analyze hostile situations such as wars and arms races [4] (see prisoner's dilemma), and also how conflict may be mitigated by repeated interaction (see tit-for-tat).
Nash equilibria are self-enforcing contracts, in which negotiation happens prior to the game being played in which each player best sticks with their negotiated move. In a Nash Equilibrium, each player is best responded to the choices of the other player. [11] Prisoners dilemma
The solutions are normally based on the concept of Nash equilibrium, and these solutions are reached by using methods listed in Solution concept. Most solutions used in non-cooperative game are refinements developed from Nash equilibrium, including the minimax mixed-strategy proved by John von Neumann. [8] [13] [20]
For instance, in the prisoner's dilemma there is only one Nash equilibrium, and its strategy (Defect) is also an ESS. Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both ( A , A ) and ( B , B ) are Nash equilibria, since players cannot do better by switching away ...
In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given. [1] The concept of a best response is central to John Nash's best-known contribution, the Nash equilibrium, the point at which each player in a game has selected the best response (or one of the best responses) to the other players ...
The most widely studied repeated games are games that are repeated an infinite number of times. In iterated prisoner's dilemma games, it is found that the preferred strategy is not to play a Nash strategy of the stage game, but to cooperate and play a socially optimum strategy.
Therefore, the strategy for the infinitely repeated prisoners’ dilemma game is a Subgame Perfect Nash equilibrium. In iterated prisoner's dilemma strategy competitions, grim trigger performs poorly even without noise , and adding signal errors makes it even worse.