Colada defango
II. 3 — POTENCIAL HUMANO
II.3. I.- ORIGINALIDAD HISTORICA
I
A B
1 2 N
I N
3, 8 -6, 9 5, -1 0, 0
I
1 2 N
I N
6, 7 3, 2 10, -5 0, 0
Answer the following questions for both technology A and technology B.
(a) Suppose the players can obtain externally enforced transfers by writ-ing a contract. Under the assumption that the court can verify exactly the outcome of production, what value can the players obtain and what contract is written? Describe both the externally and self-enforced components.
(b) Repeat part (a) under the assumption that the court can only verify whether (I, I) is played—that is, it cannot distinguish between (I, N), (N, I), and (N, N).
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(c) Explain or calculate the outcome for the setting of court-imposed breach remedies. Separately study expectation, reliance, and restitution.
Assume (0, 0) is the benchmark, nonrelationship payoff for reliance and restitution.
8. Suppose a manager (player 1) and a worker (player 2) have a contractual re-lationship with the following technology of interaction. Simultaneously and independently, the two parties each select either low (L) or high (H) effort.
A party that selects high effort suffers a disutility. The worker’s disutility of high effort (measured in dollars) is 2, whereas the manager’s disutility of high effort is 3. The effort choices yield revenue to the manager, as follows:
If both choose L, then the revenue is zero. If one party chooses L while the other selects H, then the revenue is 3. Finally, if both parties select H, then the revenue is 7. The worker’s payoff is zero minus his disutility of effort (zero if he exerted low effort), and the manager’s payoff is her revenue mi-nus her disutility of effort.
(a) Draw the normal-form matrix that represents the underlying game.
(b) If there is no external enforcement, what would be the outcome of this contractual relationship?
(c) Suppose there is external enforcement of transfers but that there is limited verifiability in that the court can only observe the revenue generated by the parties. Explain how this determines which cells of the matrix the court can distinguish between.
(d) Continuing to assume limited verifiability, what is the best outcome that the parties can achieve and what contract will they write to achieve it?
(Assume maximization of joint value.)
(e) Now assume that there is full verifiability. What outcome will be reached and what contract will be written?
9. Suppose that Shtinki Corporation operates a chemical plant, which is lo-cated on the Hudson River. Downstream from the chemical plant is a group of fisheries. The Shtinki plant emits some byproducts that pollute the river, causing harm to the fisheries. The profit Shtinki obtains from operating the chemical plant is a positive number X. The harm inflicted on the fisheries due to water pollution is measured to be Y in terms of lost profits. If the Shtinki plant is shut down, then Shtinki loses X while the fisheries gain Y.
Suppose that the fisheries collectively sue Shtinki Corporation. It is easily verified in court that Shtinki’s plant pollutes the river. However, the values X and Y cannot be verified by the court, although they are commonly known to the litigants.
Exercises 171
Suppose that the court requires the fisheries’ attorney (player 1) and the Shtinki attorney (player 2) to play the following litigation game. Player 1 is supposed to announce a number y, which the court interprets as the fish-eries’ claim about their profit loss Y. Player 2 is to announce a number x, which the court interprets as a claim about X. The announcements are made simultaneously and independently. Then the court uses Posner’s nuisance rule to make its decision.9 According to the rule, if y> x, then Shtinki must shut down its chemical plant. If xÚ y, then the court allows Shtinki to operate the plant, but the court also requires Shtinki to pay the fisheries the amount y. Note that the court cannot force the attorneys to tell the truth.
Assume the attorneys want to maximize the profits of their clients.
(a) Represent this game in the normal form by describing the strategy spaces and payoff functions.
(b) For the case in which X> Y, compute the Nash equilibria of the litiga-tion game.
(c) For the case in which X< Y, compute the Nash equilibria of the litiga-tion game.
(d) Is the court’s rule efficient?
10. Discuss a real-world example of a contractual situation with limited verifi-ability. How do the parties deal with this contractual imperfection?
11. Consider a two-player contractual setting in which the players produce as a team. In the underlying game, players 1 and 2 each select high (H) or low (L) effort. A player who selects H pays a cost of 3; selecting L costs noth-ing. The players equally share the revenue that their efforts produce. If they both select H, then revenue is 10. If they both select L, then revenue is 0. If one of them selects H and the other selects L, then revenue is x. Thus, if both players choose H, then they each obtain a payoff of 12
#
10− 3 = 2; if player 1 selects H and player 2 selects L, then player 1 gets 12#
x− 3 and player 2 gets 12#
x; and so on. Assume that x is between 0 and 10.Suppose a contract specifies the following monetary transfers from player 2 to player 1: a if (L, H) is played, b if (H, L) is played, and g if (L, L) is played.
(a) Suppose that there is limited verifiability in the sense that the court can observe only the revenue (10, x, or 0) of the team, rather than the play-ers’ individual effort levels. How does this constrain a, b, and g?
9See R. Posner, Economic Analysis of Law, 5th ed. (Boston: Little, Brown, 1997). The exercise here is from I. Kim and J. Kim, “Efficiency of Posner’s Nuisance Rule: A Reconsideration,” Journal of Institutional and Theoretical Economics 160 (2004): 327–333.
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(b) What must be true about x to guarantee that (H, H) can be achieved with limited verifiability?
12. Consider the following two-player team production problem. Each player i chooses a level of effort aiÚ 0 at a personal cost of a2i. The players se-lect their effort levels simultaneously and independently. Efforts a1 and a2 generate revenue of r= 4(a1 + a2). There is limited verifiability in that the external enforcer (court) can verify only the revenue generated by the players, not the players’ individual effort levels. Therefore, the players are limited to revenue-sharing contracts, which can be represented by two func-tions f1 : [0, )S [0, ) and f2 : [0, )S [0, ). For each player i, fi(r) is the monetary amount given to player i when the revenue is r. We require
f1(r)+ f2(r) … r for every r.
Call a contract balanced if, for every revenue level r, it is the case that f1(r)+ f2(r) = r. That is, the revenue is completely allocated between the players. A contract is unbalanced if f1(r)+ f2(r)< r for some value of r, which means that some of the revenue is destroyed or otherwise wasted.
(a) What are the efficient effort levels, which maximize the joint value 4(a1+ a2) − a21 − a22?
(b) Suppose that the players have a revenue-sharing contract specify-ing that each player gets half of the revenue. That is, player i gets (r>2) − a2i = 2(a1+ a2) − a2i. What is the Nash equilibrium of the effort-selection game?
(c) Next consider more general contracts. Can you find a balanced contract that would induce the efficient effort levels as a Nash equilibrium? If so, describe such a contract. If not, see if you can provide a proof of this result.
(d) Can you find an unbalanced contract that would induce the efficient effort levels as a Nash equilibrium? If so, describe such a contract. If not, provide a proof as best you can.
(e) Would the issues of balanced transfers matter if the court could verify the players’ effort levels? Explain.