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Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same for all players, it is listed here. Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every ...
For instance if a player prefers "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the strategy profile is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to the other players' strategies in that equilibrium ...
However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt). Further, games can have both pure strategy and mixed strategy equilibria. An easy example is the pure coordination game, where in addition to the pure strategies (A,A) and (B,B) a mixed equilibrium exists in which both ...
It would take approximately 21 k-levels to reach 0, the Nash equilibrium of the game. The guessing game depends on three elements: (1) the subject's perceptions of the level 0 would play; (2) the subject's expectations about the cognitive level of other players; and (3) the number of in-game reasoning steps that the subject is capable of ...
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). It remains unclear how expectations would form that would result in a particular equilibrium being played out.
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.
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 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 ...