Question

a) Explain what is meant by the “Prisoner’s Dilemma” game. Do players have a dominant strategy in this game?
b) Create an example of a pay-off matrix for such a game
c) Will the Nash equilibrium of this game result in the socially optimal outcome? *Explain why/why not*

Your answer will be marked according to the following categories.

• PART A
• PART B
• PART C
• General Clarity of Explanations

Answer 1

Date: Page No. a 5 an (a) Prisoner's dilemma is paradox which two participants Who are working in their OW seif interest are not able to produce optimal outpur The both participants work in their own self- interest which makes Worse -off for both of them. They both could be better off if they had cooperated in the game. Players do hot have dominant Strategi Prisoner's dilemma 11 bom cooperate s they can achieve tre dominant and optimal strategy, but as the do game, they nor know about each others Strategy therefore tha Choose strategy in their self interest which eventu makes them worse-off. NO a

(b) Now, let's take an example to understand the prisoner's Dilemma. Suppose there are two players (Player A and Player B) in a game, they both committed a crime together and there is not enough evidence to prove them guilty. They are taken to separate rooms where they are given a choice, that if they admitted that the partner did the crime then they will be free to go but the partner will be sent to prison for 3 years. If both stay silent then they both will be sent to prison for 1 year each and if they both betray each other and tell the police that the partner did the crime then they both will be sent to the prison for 2 years each. Now, let's find the nash equilibrium with the help of pay-off-matrix.

Page No. Player B Defect Cooperate Cooperale 1, 3,0 tepheld Defect 0,3 2,3

Now, if player A chose to cooperate, the player B will maximize his outcome, therefore, he will select to defect because then he will have to go to prison for 0 years. and if player A choses to defect, then the player B will also defect, because 2 years in jail is better than 3 years in jail. Similarly given the choices of player B, player A will make his choices in same way and the nash equilibrium will come out to be 2 years each in jail. Therefore, the Nash equilibrium of this game is (2,2).

(c) No, this is not the socially optimal outcome, the dominant strategy is socially optimal whereas the nash equilibrium may or may not be the socially optimal outcome. Therefore, when the strategy chosen is dominant which is when both chose to cooperate, then outcome Is socially optimal.

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