Can there be both pure and mixed Nash equilibrium?

Can there be both pure and mixed 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.

What is the difference between pure strategy and mixed strategy games?

A pure strategy involves all players making their moves simultaneously, while a mixed strategy minimizes the losses of players.

What happens when there are two Nash equilibria?

The best situation is when a game has one Nash equilibrium. If there are multiple Nash equilibria, then there is some hope that only one of them is admissible. In this case, analysis of the game indicates that the players must communicate or collaborate in some way to eliminate the possibility of regret.

Are there any equilibria in pure strategies?

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.

What is pure strategy Nash equilibria?

A pure-strategy Nash equilibrium is an action profile with the property that no single player i can obtain a higher payoff by choosing an action different from ai, given every other player j adheres to aj. For example, a game involves two players, each of whom could choose two available actions, which are X and Y.

When maxmin and Minmax value of the game are same then?

The maxmin value for one player is equal to the minmax value for the other player. By convention, the maxmin value for player 1 is called the value of the game. For both players, the set of maxmin strategies coincides with the set of minmax strategies.

How many Nash equilibria are there in pure strategies?

two pure
There are two pure-strategy equilibria, (A,A) with payoff 4 for each player and (B,B) with payoff 2 for each. The combination (B,B) is a Nash equilibrium because if either player unilaterally changes his strategy from B to A, his payoff will fall from 2 to 1. A famous example of a coordination game is the stag hunt.