1.Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 24 units of utility from a vote for their positions (and lose 24 units of utility from a vote against their positions). However, the bother of actually voting costs each 12 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward.
Mrs. Ward
VoteDon’t Vote
Mr. Ward Vote Mr. Ward: -12, Mrs. Ward: -12 Mr. Ward: 12, Mrs. Ward: -24
Don’t VoteMr. Ward: -24, Mrs. Ward: 12Mr. Ward: 0, Mrs. Ward: 0
The Nash equilibrium for this game is for Mr. Ward to vote/not vote and for Mrs. Ward to vote/not vote Under this outcome, Mr. Ward receives a payoff of _____
units of utility and Mrs. Ward receives a payoff of ______
units of utility.
Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow’s election.
True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question.
True
False
This agreement not to vote is/is not a Nash equilibrium.
2. Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival 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. If the two companies select different technologies, Microsoft’s payoff is 4 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility.
Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously.
Microsoft
Technology ATechnology B
Rival Technology A Rival:
, Microsoft Rival:
, Microsoft
Technology BRival:
, Microsoft Rival:
, Microsoft
True or False: There is an equilibrium for this game in pure strategies.
4. Every year, management and labor renegotiate a new employment contract by sending their pr
oposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $2 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time.
Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.)
Management (M)
No LawyerLawyer
Labor (L) No Lawyer L:
, M: L:
, M:
LawyerL:
, M: L:
, M:
The Nash equilibrium for this game is for Management to Hire/not hire a lawyer, and for Labor to hire/not hire a lawyer.
5 . Individual Problems 15-6
Consider a sequential-move game in which an entrant is considering entering an industry in competition with an incumbent firm. If the entrant does not enter (“Out”), the incumbent firm earns a payoff of 10, while the entrant earns a payoff of 0. If the entrant enters (“In”), then the incumbent can either accommodate or fight. If the incumbent accommodates, both earn a payoff of 5. If the incumbent fights, then the entrant can either leave the industry (“Withdraw”) or remain in it (“Stay”). If the entrant stays, both earn a payoff of –5. If the entrant withdraws, the entrant earns a payoff of –1, and the incumbent earns a payoff of 8. The extensive form of the game is depicted in the following figure, where the payoffs are of the form (Entrant Payoff, Incumbent Payoff).
EntrantIncumbent(5,5)(-1,8)(0,10)(-5,-5)InOutAccommodateFightEntrantWithdrawStay
True or False: The equilibrium for this game is {In, Fight, Stay}.
False/
True
6. Two equal-sized newspapers have an overlap circulation of 10% (10% of the subscribers subscribe to both newspapers). Advertisers are willing to pay $23 to advertise in one newspaper but only $44 to advertise in both, because they’re unwilling to pay twice to reach the same subscriber. Suppose the advertisers bargain by telling each newspaper that they’re going to reach agreement with the other newspaper, whereby they pay the other newspaper $21 to advertise.
According to the nonstrategic view of bargaining, each newspaper would earn
of the $21 in value added by reaching an agreement with the advertisers. The total gain for the two newspapers from reaching an agreement is
.
Suppose the two newspapers merge. As such, the advertisers can no longer bargain by telling each newspaper that they’re going to reach agreement with the other newspaper. Thus, the total gains for the two parties (the advertisers and the merged newspapers) from reaching an agreement with the advertisers are $21.
According to the nonstrategic view of bargaining, each merged newspaper will earn
in an agreement with the advertisers. This gain to the merged newspaper is less/greater than the total gains to the individual newspapers pre-meger.
7. Pharmaceutical Benefits Managers (PBMs) are intermediaries between upstream drug manufacturers and downstream insurance companies. They design formularies (lists of drugs that insurance will cover) and negotiate prices with drug companies. PBMs want a wider variety of drugs available to their insured populations, but at low prices. Suppose that a PBM is negotiating with the makers of two nondrowsy allergy drugs, Claritin and Allegra, for inclusion on the formulary. The “value” or “surplus” created by including one nondrowsy allergy drug on the formulary is $80 million, but the value of adding a second drug is only $8 million.
Assume the PBM bargains by telling each drug company that it’s going to reach an agreement with the other drug company.
Under the non-strategic view of bargaining, the PBM would earn a surplus of
million, while each drug company would earn a surplus of
million.
Now suppose the two drug companies merge. What is the likely postmerger bargaining outcome?
Under the nonstrategic view of bargaining, the PBM would earn a surplus of
million, while the merged drug company would earn a surplus of
million.
