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 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?