Suppose that Shtinki Corporation operates a chemical plant, which is located 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. 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 fisheries' 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 x Ú 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 litigation game.
(c) For the case in which X
(d) Is the court's rule efficient?