Question

Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that:

(i) There is exactly one pure strategy Nash equilibrium.

(ii) There are exactly two pure strategy Nash equilibria.

(iii) There are exactly three pure strategy Nash equilibria.

(iv) There are exactly nine pure strategy Nash equilibria

Answer 1

NASH EQUILIBRIUM

Nash equilibrium is concept in the game theory where the optimal outcome of a game is where there is no incentive to deviate from their initial strategy.More specifically Nash equilibrium is a concept of game theory where the optimal outcome of a game is one player has no incentive to deviate from his chosen strategy after considering an opponents choice.Overall an individual can receive an incremental benefit from changing actions, assuming other players remaining constant in their strategies.A game may have multiple Nash equilibria or none at all.

For example imagine a game between Tom and Sam .In this simple game both players can choose strategy A ,to receive $1, or strategy B to lose $1.Logically both players chose strategy A an receive a payoff $1. If you revealed Sam's strategy to Tom and vice versa, you see that no players will deviate from the original choice.Knowing the other players move means little and doesn't change either players behavior.The outcome A , A represents a Nash equilibrium.