a. What is the Prisoners dilemma problem in pricing? Explain. What strategies can a firm undertake to avoid this prisoners dilemma problem?

b. We looked at the team members dilemma which is an example of a prisoners 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 3: Simultaneous and Sequential game

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 A B C

A 250, 200 100, 50 170, 280

Player 1

B 260, 140 270,270 130, 130

C 265, 300 120, 130 125, 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 prisoners 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?