3. (10 points) War (Ch 15, Problem 7) Two players, 1 and 2, fight over a single indivisible object worth V' > 0 to each of them. Each player invests in becoming more powerful: denote by x;, a nonnegative number, the investment of player i. Given investments (x1,x2), player i 's probability of winning the object is if z1 + 29> 0 pi (Z1,22) = { Ti +%j : if X =To = () Each player 's utility function is ui(zi, 25) = pi (21, 22) V 2. Find the pure-strategy Nash equilibrium