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If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria.If both players have a strictly dominant strategy, the game has only one unique Nash equilibrium, referred to as a "dominant strategy equilibrium".
A mixed strategy is an assignment of a probability to each pure strategy. When enlisting mixed strategy, it is often because the game does not allow for a rational description in specifying a pure strategy for the game. This allows for a player to randomly select a pure strategy. (See the following section for an illustration.)
If both A and B have strictly dominant strategies, there exists a unique Nash equilibrium in which each plays their strictly dominant strategy. In games with mixed-strategy Nash equilibria, the probability of a player choosing any particular (so pure) strategy can be computed by assigning a variable to each strategy that represents a fixed ...
In game theory, normal form is a description of a game. Unlike extensive form , normal-form representations are not graphical per se , but rather represent the game by way of a matrix . While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria , some information is lost as compared to extensive ...
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type.
Equilibrium selection is a concept from game theory which seeks to address reasons for players of a game to select a certain equilibrium over another. The concept is especially relevant in evolutionary game theory, where the different methods of equilibrium selection respond to different ideas of what equilibria will be stable and persistent for one player to play even in the face of ...
Any game that satisfies the following two conditions constitutes a Deadlock game: (1) e>g>a>c and (2) d>h>b>f. These conditions require that d and D be dominant. (d, D) be of mutual benefit, and that one prefer one's opponent play c rather than d. Like the Prisoner's Dilemma, this game has one unique Nash equilibrium: (d, D).
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten.A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. 1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since ...