LITGY 3. Two players compete for a prize whose value is R. The probability that player 1 wins is p1 = erty' and the probability that player 2 wins is p2 = and , where r and y are dollar values of effort spent by players 1 and 2 to win the prize, and where 0 2 1 measures the advantage to player 1. The expected utility of player 1 is up = piR -r and the expected utility of player 2 is u2 = pzR- y. (a) Solve for the Nash equilibrium expenditures. Hint: Solve each first-order-condition for (Or + y)- and use these to show how r is related to y, then use either equation to solve for r. 5 marks] (b) Suppose that 0 = 1. What fraction of the rents R is expended by the two parties in total in an attempt to win R? How does this change if 0 = 27 Explain. [5 marks]