QUESTION 1

a.What is the Prisoner's dilemma problem in pricing?Explain. What strategies can a firm undertake to avoid this prisoner's dilemma problem?

b. We looked at the "team member's dilemma" which is an example of a prisoner's dilemma in a single period game but may lead to cooperation in a multi-period game.

Consider a one period game where two team members have two strategies - to give high effort or low effort. If both give high effort the payoff is $10,000 for each. If they both give low effort their payoff is $2000 each. If one gives low effort and the other high effort, the one who gives low effort gets $11000 and the one who gives high effort gets 0.

Write out a multi period payoff matrix by using the technique used in class.Assume that one who starts with low effort continue with low effort and the others use a "tit for tat" strategy.Compute a "break-even probability" of future interaction that would induce cooperation.Explain what this probability means.

QUESTION 2

Consider the following payoff matrix, where the payoffs are profits in thousand $.

Explanation of payoff: If Player 1 chooses Strategy A and player 2 chooses Strategy B then Player 1 gets $100,000 and Player 2 gets $50,000

Player 2

Strategy ABC

A250, 200100, 50170, 280

Player 1

B260, 140270,270130, 130

C265, 300120, 130125, 140

1.Find the Nash equilibrium if the players make the decisions simultaneously.

2.Are there any dominant strategies in the game?

3.Is this a prisoner's dilemma type problem? Explain why.

4.Find the outcome if both players are risk averse and choose a maxi-min strategy.

5.Now consider the game as sequential.How much would player 2 invest to be the first mover? Is there any potential for side payments? (one player offering the other to be 2^nd mover) If so, who will pay and how much?