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For finitely repeated games, if a stage game has only one unique Nash equilibrium, the subgame perfect equilibrium is to play without considering past actions, treating the current subgame as a one-shot game. An example of this is a finitely repeated Prisoner's dilemma game. The Prisoner's dilemma gets its name from a situation that contains ...
The blue equilibrium is not subgame perfect because player two makes a non-credible threat at 2(2) to be unkind (U). The Nash equilibrium is a superset of the subgame perfect Nash equilibrium. The subgame perfect equilibrium in addition to the Nash equilibrium requires that the strategy also is a Nash equilibrium in every subgame of that game.
A perfect-subgame equilibrium occurs when there are Nash Equilibria in every subgame, that players have no incentive to deviate from. [2] In both subgames, it benefits the responder to accept the offer. So, the second set of Nash equilibria above is not subgame perfect: the responder can choose a better strategy for one of the subgames.
A Nash equilibrium is a strategy profile (a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (cooperate, defect) specifies that prisoner 1 plays cooperate and prisoner 2 plays defect) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) .
If a node is contained in the subgame then so are all of its successors. If a node in a particular information set is in the subgame then all members of that information set belong to the subgame. It is a notion used in the solution concept of subgame perfect Nash equilibrium, a refinement of the Nash equilibrium that eliminates non-credible ...
The unique symmetric Nash equilibrium is defined by the following survival function for t: [6] = (/) The value (), for a player i whose opponent values the resource at over time t, is the probability that t ≥ x. This strategy does not guarantee the win for either player.
It is called a coalition subgame-perfect equilibrium if no coalition can gain from deviating after any history. [9] With the limit-of-means criterion, a payoff profile is attainable in coalition-Nash-equilibrium or in coalition-subgame-perfect-equilibrium, if-and-only-if it is Pareto efficient and weakly-coalition-individually-rational. [10]
Nash equilibrium: Superset of: Stochastically stable equilibrium, Stable Strong Nash equilibrium: Intersects with: Subgame perfect equilibrium, Trembling hand perfect equilibrium, Perfect Bayesian equilibrium: Significance; Proposed by: John Maynard Smith and George R. Price: Used for: Biological modeling and Evolutionary game theory: Example ...