Exercise 2.23-✰✰✰ Challenging Question ★★★. The Mondevil Corporation operates a chemical plant, which is located on the banks of the Sacramento river. Downstream from the chemical plant is a group of fisheries. The Mondevil plant emits by-products that pollute the river, causing harm to the fisheries. The profit Mondevil obtains from operating the chemical plant is $II > 0. The harm inflicted on the fisheries due to water pollution is equal to $L> 0 of lost profit [without pollution the fisheries' profit is $A, while with pollution it is $(A - L)]. Suppose that the fisheries collectively sue the Mondevil Corporation. It is easily verified in court that Mondevil's plant pollutes the river. However, the values of II and L cannot be verified by the court, although they are commonly known to the litigants. Suppose that the court requires the Mondevil attorney (Player 1) and the fisheries' attorney (Player 2) to play the following litigation game. Player 1 is asked to announce a number x > 0, which the court interprets as a claim about the plant's profits. Player 2 is asked to announce a number y≥ 0, which the court interprets as the fisheries' claim about their profit loss. The announcements are made simultaneously and independently. Then the court uses Posner's nuisance rule to make its decision (R. Posner, Economic Analysis of Law, 9th edition, 1997). According to the rule, if y> x, then Mondevil must shut down its chemical plant. If xy, then the court allows Mondevil to operate the plant, but the court also requires Mondevil to pay the fisheries the amount y. Note that the court cannot force the attorneys to tell the truth: in fact, it would not be able to tell whether or not the lawyers were reporting truthfully. Assume that the attorneys want to maximize the payoff (profits) of their clients. (a) Represent this situation as a strategic-form game by describing the strategy set of each player and the payoff functions. (b) Is it a dominant strategy for the Mondevil attorney to make a truthful announce- ment (i.e. to choose x = II)? [Prove your claim.]