Question

4. Define a Nash equilibrium intuitively-a mathematical definition is not expected. Why is it always a conditional equilibrium? (10)

Answer 1

Answer) Nash equilibrium - Strategy chosen by a player such that she does best given what other player has chosen.

Dominant strategy - A strategy chosen by a player irrespective of what other player does.

In case of, prisoner's dilemma game it is observed that the best setbod strategy may not be chosen as an equilibrium strategy. This is because under the prisoner's dilemma sub-optimum set results in the convergence of nash strategies.

In the above example, Prisoner 1 chooses to confess if prisoner 2 chooses to confess because otherwise, one will spend ten years in jail while confessing results in 5 years. Similarly, if prisoner 2 chooses not to confess the best strategy for 1 is to confess because it results in no imprisonment. Therefore nash strategies for 1 in both cases is confess which means confess becomes the Dominant strategy for 1. In the same way, confess is also a dominant strategy for 2 because no matter what one chooses the best strategy for 2 is always to confess when the players will strategize to make their optimum choice they realize that no matter what they choose a dominant strategy for other is always confess given the other player chooses to confess their best strategy is to confess. The intersection of two strategies is nash equilibrium. Given player 1 has chosen the best strategy for 2 is to choose to confess & given two has chosen to confess the best strategy for 1 is to choose to confess. This makes (confess, confess) a Nash equilibrium for this game.

It is called sub-optimum because if both had chosen not to confess then their imprisonment will be for a lesser time period.

In the above example of the Prisoners Dilemma, we see that the condition is always linked with the equilibrium. The strategy is interdependent among themselves that's why it's conditional equilibrium.

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