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In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players ...
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) .
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.
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 ...
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]
The one-shot deviation principle (also known as single-deviation property [1]) is the principle of optimality of dynamic programming applied to game theory. [2] It says that a strategy profile of a finite multi-stage extensive-form game with observed actions is a subgame perfect equilibrium (SPE) if and only if there exist no profitable single deviation for each subgame and every player.
The blue equilibrium is not subgame perfect because player two makes a non-credible threat at 2(2) to be unkind (U). A non-credible threat is a term used in game theory and economics to describe a threat in a sequential game that a rational player would not actually carry out, because it would not be in his best interest to do so.