What kind of game has no Nash equilibrium?

What kind of game has no Nash equilibrium?

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). Further, games can have both pure strategy and mixed strategy equilibria.”

When would there be no Nash equilibrium?

Nash equilibria need not exist if the set of choices is infinite and non-compact. An example is a game where two players simultaneously name a number and the player naming the larger number wins.

Can a game have no mixed strategy equilibrium?

There is no non-pure mixed strategy Nash equilibrium because both players have strictly dominant strategies. Any possible mix with a positive weight on cooperating would be strictly dominated by a pure strategy of defecting.

Is there Nash equilibrium without dominant strategy?

A Nash equilibrium is conditional upon the other player’s best strategy, but a dominant strategy is unconditional. A game has a Nash equilibrium even if there is no dominant strategy (see example below). It is also possible for a game to have multiple Nash equilibria.

Can there be no pure Nash equilibrium?

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. Instead, the unique Nash equilibrium of this game is in mixed strategies: each player chooses heads or tails with equal probability.

Can a game have both pure and mixed strategy?

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 players play either strategy with probability 1/2.

What is pure Nash equilibrium?

In plain terms, a pure Nash equilibrium is a strategy profile in which no player would benefit by deviating, given that all other players don’t deviate. Some games have multiple pure Nash equilib ria and some games do not have any pure Nash equilibria.