ECON-112 Principles of Microeconomics
Problem Set #8 (Practice Only)-SOLUTIONS Posted: Wednesday, December 4th, 2013 Due Date: None
1. Mankiw (6th edition), Chp17, Problem 6 (page 370)
a. The payoffs are:
Your Decision Work You get 15 units of happiness Work Classmate gets 15 units of happiness You get 5 units of happiness Shirk Classmate gets 30 units of happiness Shirk You get 30 units of happiness Classmate gets 5 units of happiness You get 10 units of happiness Classmate gets 10 units of happiness
Classmate’ s Decision
b. The likely outcome is that both of you will shirk. If your classmate works, you’re better off shirking, because you would rather have 30 units of ...view middle of the document...
The playoff matrix for this game is:
Player One’s Decision
Take Drug Don’t Take Drug
Player Two’s Decision Take Drug Don’t Take Drug Player 1 gets 5,000 – X Player 1 gets 10,000 - X Player 2 gets 5,000 – X Player 2 gets 0 Player 1 gets 0 Player 1 gets 5,000 Player 2 gets 10,000 Player 2 gets 5,000 X
b. Taking the drug will be a dominant strategy for each player as long as X is less than 5,000. c. Making the drug safer (lowering X) raises the likelihood of taking the drug because it increases the payoff.
in addition…. a. Assume that the health cost of the drug is equal to $1000 for one of the athletes, and $10000 for the other athlete. Draw the payoff matrix. Does either athlete have a dominant strategy? Are there any Nash Equilibria? If so, what are the N.E. strategies and payoffs?
Player One’s Decision
Take Drug Don’t Take Drug
Player Two’s Decision Take Drug Don’t Take Drug Player 1 gets 4,000 Player 1 gets 9,000 Player 2 gets -5,000 Player 2 gets 0 Player 1 gets 0 Player 1 gets 5,000 Player 2 gets 0 Player 2 gets 5,000
Best responses are in bold. It is dominant for player 1 to take the drug, but for player 2 to not take the drug, since it is very costly for player 2 to take the drug. There is 1 N.E…..Player 1 takes the drug, player 2 does not take the drug, and player 1 gets 9000 and player 2 gets 0.
b. Assume that the health care cost of the drug is equal to $1000 for both. Also, assume that if one athlete uses the drug and the other does not, then the drug-free athlete reports the drug user, and then both athletes win nothing. Draw the payoff matrix. Does either athlete have a dominant strategy? Are there any Nash Equilibria? If so, what are the N.E. strategies and payoffs?
Player One’s Decision
Take Drug Don’t Take Drug
Player Two’s Decision Take Drug Don’t Take Drug Player 1 gets 4,000 Player 1 gets -1,000 Player 2 gets 4,000 Player 2 gets 0 Player 1 gets 0 Player 1 gets 5,000 Player 2 gets -1,000 Player 2 gets 5,000
Best responses are in bold. Neither athlete has a dominant strategy. In fact, there are 2 N.E.’s in this game. 1. Both players take the drug, and both get 4000 2. Both players do not take the drug, and both get 5000 This is an example of a coordination game, but clearly they would both decide to not take th drug if they could get together beforehand. c, Assume that the health cost of the drug is equal to x for both athletes. Also, assume that if one athlete uses the drug and the other does not then the drug-free athlete reports the drug user, and all the winnigs are now transferred to the drug free athlete. Draw the payoff matrix. Does either athlete have a dominant strategy? Are there any Nash Equilibria? If so, what are the N.E. strategies and payoffs?
Player One’s Decision
Take Drug Don’t Take Drug
Player Two’s Decision Take Drug Don’t Take Drug Player 1 gets 5,000 – X Player 1 gets -X Player 2 gets 5,000 – X Player 2 gets 10,000 Player 1 gets 10,000 Player 1 gets 5,000...
