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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.
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) .
For the entire game Nash equilibria (DA, Y) and (DB, Y) are not subgame perfect equilibria because the move of Player 2 does not constitute a Nash equilibrium. The Nash equilibrium (UA, X) is subgame perfect because it incorporates the subgame Nash equilibrium (A, X) as part of its strategy. [3] To solve this game, first find the Nash ...
The Nash equilibrium was the most common agreement (mode), but the average (mean) agreement was closer to a point based on expected utility. [11] In real-world negotiations, participants often first search for a general bargaining formula, and then only work out the details of such an arrangement, thus precluding the disagreement point and ...
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 ...
In game theory, a strong Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively deviate in a way that strictly benefits all of its members, given that the actions of the other players remain fixed. This is in contrast to simple Nash equilibrium, which considers only ...
The Lemke–Howson algorithm is an algorithm that computes a Nash equilibrium of a bimatrix game, named after its inventors, Carlton E. Lemke and J. T. Howson. [1] It is said to be "the best known among the combinatorial algorithms for finding a Nash equilibrium", [2] although more recently the Porter-Nudelman-Shoham algorithm [3] has outperformed on a number of benchmarks.
There is a unique pure strategy Nash equilibrium. This equilibrium can be found by iterated elimination of weakly dominated strategies. [4] Intuitively, guessing any number higher than 2/3 of what you expect others to guess on average cannot be part of a Nash equilibrium. The highest possible average that would occur if everyone guessed 100 is ...