Question 3. Each of two travelers takes a suitcase containing, an identical object on a ight. The value ofthe object is known to be between $180 and $300. The suitcases are lost, and the airline must compensate the travelers. The airline asks each traveler to name an integer between 180 and 300. Each traveler gets (in dollars) the smaller of the numbers chosen, and, if the numbers differ, in addition $5 is transferred from the traveler who names the larger number to the one who names the smaller number. For example, when both travelers name 200, they both will receive $200. Instead, when Traveler 1 names 200 and Traveler 2 names a number 250, Traveler 1 will receive $205, and Traveler 2 will receiVe $195. Write n1 for Traveler 1's action and (12 for Traveler 2's action. a) Write down the amount of compensation that each traveler receives for different pairs of numbers named, that is, compensation pairs (111011. a2),M2(a1, oz for 180 5 a1, a2 5 300. (5 pts) (Hint: Focus on Traveler 1 and consider three cases: (1) r11 0.2.) b) Show that a1 = a2 = 180 is a Nash equilibrium. (10 pts) 0) Show that there are no other pure~strategy Nash equilibria other than a1 2 a2 2 180. (10 pts) Question 4. The market demand curve in a commodity chemical industry is given by Q = 600 - 31', where Q is the quantity demanded per month and P is the market price in dollars. Firms in this industry supply quantities every month, and the resulting market price occurs at the point at which the quantity demanded equals the total quantity supplied. Suppose there are two rms in this industry, Firm 1 and Firm 2. Each rm has an identical constant marginal cost of $80 per unit. a) nd the Cournot equilibrium quantities for each firm and the Cournet equilibrium price. (10 pts) b) ssuming that Firm 1 is the Stackelberg leader, find the Stackelberg equilibrium quantities for each firm and the Stackelberg equilibrium price. (10 M) c) Ca ulate and compare the prot of each firm under the Coumot and Stackelberg equilibria. Under which equilibrium is overall industry prot the greatest? (5 pts) ------ END OF PAPER