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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. This eliminates all non-credible threats , that is, strategies that contain non-rational moves in order to make the counter-player change their strategy.
The two pure strategy Nash equilibria are unfair; one player consistently does better than the other. The mixed strategy Nash equilibrium is inefficient: the players will miscoordinate with probability 13/25, leaving each player with an expected return of 6/5 (less than the payoff of 2 from each's less favored pure strategy equilibrium).
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) .
Defection always results in a better payoff than cooperation, so it is a strictly dominant strategy for both players. Mutual defection is the only strong Nash equilibrium in the game. Since the collectively ideal result of mutual cooperation is irrational from a self-interested standpoint, this Nash equilibrium is not Pareto efficient.
Further, it is possible for a game to have a Nash equilibrium that is resilient against coalitions less than a specified size k. CPNE is related to the theory of the core. Confusingly, the concept of a strong Nash equilibrium is unrelated to that of a weak Nash equilibrium. That is, a Nash equilibrium can be both strong and weak, either, or ...
Strict stationary equilibria: [6] A Nash equilibrium is called strict if each player strictly prefers the infinite sequence of outcomes attained in equilibrium, over any other sequence he can deviate to. A Nash equilibrium is called stationary if the outcome is the same in each time-period. An outcome is attainable in strict-stationary ...
A pure Nash Equilibrium is when no one can gain a higher payoff by deviating from their move, provided others stick with their original choices. 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 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 ...