## What are the Nash equilibria in this game?

The Nash equilibrium is a decision-making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy. In the Nash equilibrium, each player’s strategy is optimal when considering the decisions of other players.

**How many Nash equilibria are there in the prisoner’s dilemma?**

So the only Nash-equilibrium in the prisoner’s dilemma is for both of you to defect. This does not mean that this is the best outcome available to you. This equilibrium leads you both to very bad outcome, where each of you spends five years in prison.

**Is there always a Nash equilibrium?**

There does not always exist a pure Nash equilibrium.

### What is rectangular game?

Rectangular game theory is applied to the response of organisms to random environmental changes: A hypothetical example of the response of a facultative algae to random changes in illumination is analyzed. Two strategies are discussed: Bayes’ risk and maximin. It is shown how to detect such strategies in populations.

**Do all games have mixed Nash equilibrium?**

Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed 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.

**Is there Nash equilibrium in social dilemma?**

A social dilemma is a normal-form game with two aproperties: 1. there is a unique Nash equilibrium sN, which is a pure strategy profile; 2.

#### What is a 2×2 game without saddle point explain?

Suppose that a 2×2 game has no saddle point. Suppose the game has the following pay-off matrix. Since this game has no saddle point, the following condition shall hold: Max {Min {a , b}, Min {c , d }} ≠ Min {Max {a , c}, Max {b, d}} In this case, the game is called a mixed game.