Problems: Chapter 15

15‐1

Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.

15‐3

Microsoft and a smaller rival often have to select from one of two competing technologies. The rivals always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. Describe the equilibrium of this game.

15‐4

The below figure represents the potential outcomes of your first salary negotiation after graduation. Assuming this is a sequential move game with the employer moving first, indicate the most likely outcome. Does the ability to move first give the employer an advantage? If so, how? As the employee, is there anything you could do to realize a higher payoff?

15-6

In the text, we considered a sequential move game in which an entrant was considering entering an industry in competition with an incumbent firm (Figure15.1). Consider now that the entrant, if fought, has the possibility of withdrawing from the industry (at a loss of 1 for the entrant and a gain of 8 for the incumbent), or staying (at a loss of 5 for each player). What is the equilibrium of this game? Discuss if the entrant is better off with or without the ability to withdraw.

Employer

low salary offer

employee walks

employer get 0

employee gets 0

employee accepts

employer gets 100

employee gets 75

high salary offer

employee walks

employer gets 0

employee get 0

employee accepts

employee gets 100

employer gets 75