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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.
Adding repetition to the game introduces a focal point at the Nash equilibrium solution of 0. This was shown by Camerer as, “[when] the game is played multiple times with the same group, the average moves close to 0.” [ 5 ] Introducing the iterative aspect to the game forces all players onto higher levels of thinking which allows them all ...
The solutions are normally based on the concept of Nash equilibrium, and these solutions are reached by using methods listed in Solution concept. Most solutions used in non-cooperative game are refinements developed from Nash equilibrium , including the minimax mixed-strategy proved by John von Neumann .
The two pure strategy Nash equilibria are unfair; one player consistently does better than the other. 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).
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.
While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt ...
The decision of each player can be viewed as determining two angles. Symmetric Nash equilibria that attain a payoff value of / for each player is shown, and each player volunteers at this Nash equilibrium. Furthermore, these Nash equilibria are Pareto optimal. It is shown that the payoff function of Nash equilibria in the quantum setting is ...
A pure Nash Equilibrium is when no one can gain a higher payoff by deviating from their move, provided others stick with their original choices. Nash equilibria are self-enforcing contracts, in which negotiation happens prior to the game being played in which each player best sticks with their negotiated move.