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Formally, a strong Nash equilibrium is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members. [19] However, the strong Nash concept is sometimes perceived as too "strong" in that the environment allows for unlimited private communication.
This example is a two-person non-cooperative non-zero sum (TNNC) game with opposite payoffs or conflicting preferences. [14] Because there are two Nash equilibria, this case is a pure coordination problem with no possibility of refinement or selection. [12]
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) .
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 ...
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.
Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium. [1] This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. In other words, there is no pair of pure strategies such that neither player ...
An ESS is a refined or modified form of a Nash equilibrium. (See the next section for examples which contrast the two.) In a Nash equilibrium, if all players adopt their respective parts, no player can benefit by switching to any alternative strategy. In a two player game, it is a strategy pair.
Example 2: Two-Stage Repeated Game with Unique Nash Equilibrium Example 2 shows a two-stage repeated game with a unique Nash equilibrium. Because there is only one equilibrium here, there is no mechanism for either player to threaten punishment or promise reward in the game's second round.