Question

Alex and Owen are playing a game of simultaneous moves where they are deciding which concert they will attend on Saturday night. Two musicians are performing that night locally, Artist 1 and Artist 2. Alex prefers to go to Artist 1 with Owen rather than Artist 2 with Owen, and he prefers going to Artist 2 with Owen rather than going to Artist 2 alone. Moreover, he prefers going to Artist 1 alone rather than going to Artist 2 with Owen. Owen prefers going to Artist 2 with Alex rather than Artist 1 with Alex and he prefers going to Artist 1 with Alex rather than going to Artist 1 alone. Moreover, he prefers going to Artist 1 with Alex rather than going to Artist 2 alone.

a) Write down the payoff matrix for the above game. Use payoffs (utility levels) that reflect the above assumptions. You can use any numbers such that the above assumptions are not violated. (1 mark)

b) Find the best response functions for Alex and for Owen. Does Alex have a dominant strategy? What about Owen? (1 mark)

c) Find all the Nash Equilibria in the game. (1 mark) Which of these lead to Pareto 1 efficient outcomes? Is there an outcome that Alex would prefer that is not a Nash equilibrium? Is there an outcome that Owen would prefer that is not a Nash equilibrium? (1 mark)

d) Suppose that the game is played sequentially and Alex moves first. Write the game in its extensive form and find all subgame-perfect Nash equilibria. (1 mark)

e) Suppose that the game is played sequentially and Owen moves first. Write the game in its extensive form and find all find all subgame-perfect Nash equilibria. (1 mark)

f) Are any of the Nash equilibria that you found in part c) based on empty threats in the sequential games in part d) or in part e)? Explain your answer briefly. (1 mark)

Answer 1