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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.
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 ...
Figure 7 - Reaction correspondence for 2x2 coordination games. Nash equilibria are at points where the two players' correspondences cross. The pure Nash equilibria are the points in the bottom left and top right corners of the strategy space, while the mixed Nash equilibrium lies in the middle, at the intersection of the dashed lines.
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-form representations.
However, many of the commonly studied 2x2 games are at least ordinally symmetric. The standard representations of chicken , the Prisoner's Dilemma , and the Stag hunt are all symmetric games. Formally, in order for a 2x2 game to be symmetric, its payoff matrix must conform to the schema pictured to the right.
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) .
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 player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change their strategy.
Looking at this matrix, we can conclude a few basic observations. [15] For all scenarios, there will be a loser and a winner. This is a zero sum game where the pay out to the winner is equal to the loss of the loser. There is no Pure Strategy Nash Equilibrium.