Can a game have multiple Nash equilibriums?

Can a game have multiple Nash equilibriums?

More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from their chosen strategy after considering an opponent’s choice. A game may have multiple Nash equilibria or none at all.

Can there be a Nash equilibrium without a dominant strategy?

Yes, a game can have a Nash equilibrium even though neither player has a dominant or dominated strategy. In fact, every game has a Nash equilibrium, possibly in mixed strategies. The game of Chicken is an example of a game with no dominant or dominated strategies but which has a Nash equilibrium.

How do you know when there is no Nash equilibrium?

To find the Nash equilibria, we examine each action profile in turn. Firm 2 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X. Thus this action profile is not a Nash equilibrium. Firm 1 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X.

What is the non cooperative Nash equilibrium?

Nash Equilibrium is a game theory. The concept that determines the optimal solution in a non-cooperative game in which each player lacks any incentive to change his/her initial strategy. Under the Nash equilibrium, a player does not gain anything from deviating from their initially chosen strategy.

Can a game have no dominant strategy?

In game theory, a dominant strategy is the course of action that results in the highest payoff for a player regardless of what the other player does. Not all players in all games have dominant strategies; but when they do, they can blindly follow them.

Why is game theory not always accurate predictor of real world situations?

Why might game theory not always be an accurate predictor of​ real-world situations? We do not always know the exact​ payoffs, since payoffs involve attitudes and feelings as well as monetary gains. The​ players, the​ strategies, the payoffs.

How many Nash equilibria can a game have?

two Nash equilibria
Neither player can increase her payoff by choosing an action different from her current one. Thus this action profile is a Nash equilibrium. We conclude that the game has two Nash equilibria, (I,I) and (A,A).

Can there be Nash equilibrium without dominant strategy?