Prof. Bryan Caplan
HW #5 (will NOT be collected or graded)
1. Determine the critical value of b for Bertrand collusion enforced by punishments of just ONE turn of Nash reversion.
2. Determine the critical value of b for Cournot collusion enforced by punishments of just ONE turn of Nash reversion.
3. Consider the voluntary donation game in part II of the Week 6 notes. Determine the critical value of b required to sustain the socially optimal donation level using trigger strategies.
4. Suppose there are 2 players deciding whether to contribute to a public good. The public good is discrete: it is produced at the optimal level so long as 1 person contribute. Contributing costs the individual who contributes C, and 0 otherwise. If the public good is produced, everyone gets a benefit of B; otherwise they get a benefit of 0. B>C. Calculate and explain the PSNE of this game. Informally, what would the MSNE look like?
5. Characterize the PSNE of the game in problem 4 if there are N players and (N-k) people must contribute to create the public good.
6. Diagram a situation where there are large externalities but laissez-faire still yields a perfectly efficient result. Suggest a real-world example.
7. Suppose you have a 2-player version of problem #3, with one difference: Each agent cares somewhat about the other, so they maximize Ui=ciD+a*cjD, with 0<a<1. How does your answer to #3 change, and why? (Hint: You have two symmetric equations in two unknowns).
8. Present and explain a novel application of:
a. Coordination games
b. Hawk/Doves games
9. Where are you most likely to see full rent-dissipation? When are you least like to see it?
10. Carefully explain and diagram the welfare properties of the "worse-case" of monopoly, where there is allocative, productive, AND lobbying inefficiency.