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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.
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 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.
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) .
A Bayesian Nash Equilibrium (BNE) is a Nash equilibrium for a Bayesian game, which is derived from the ex-ante normal form game associated with the Bayesian framework. In a traditional (non-Bayesian) game, a strategy profile is a Nash equilibrium if every player's strategy is a best response to the other players' strategies. In this situation ...
The potential function is a useful tool to analyze equilibrium properties of games, since the incentives of all players are mapped into one function, and the set of pure Nash equilibria can be found by locating the local optima of the potential function. Convergence and finite-time convergence of an iterated game towards a Nash equilibrium can ...
In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash Equilibria. He won the Leroy P. Steele Prize in 1999. In 1994, he received the Nobel Memorial Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten ) for his game theory work as a Princeton graduate ...
A family of Nash equilibria for 3-player Kuhn poker is known analytically, which makes it the largest game with more than two players with analytic solution. [1] The family is parameterized using 4–6 parameters (depending on the chosen equilibrium).