- W W W W W W W e /T I Q1: Ultimatum Game (1 point) $0 $1 $2 $3 $4 $5 $6 $7\\ $8 $9 $10 A R ($6,54) ($0,%0) Imagine that the ultimatum game is played with two utilitarian agents who each have utility functions u(l, II) = /T + +/TI. In this representation, the agent offering the ultimatum gains a payoff equal to Ie [0, 10] (as chosen by the agent) if the receiver accepts the ultimatum and I = Q if the ultimatum is rejected. The agent deciding whether to accept or reject the ultimatum receives payoff IT = 10 I if accepting and I'I = 0 if rejecting the ultimatum. Find the unique subgame-perfect equilibrium for this game. Q2: Game Theory (1 point) Consider the following two player game: Player 2 Player 2 C D Player 1 C ($16, $16) ($0, $25) Player 1 D ($25, $0) ($9, $9) Each of the two individuals playing this game count their own payoff as x and the payoff to the other player as y. Find the Nash equilibria in pure strategies for this game when played by: A. Two egoists, for whom u(z, y) = \\/E B. Two utilitarians, for whom u(z,y) = v/ + / C. Two enviers, for whom u(z, y) = /& /Y D. Two Rawlsians, for whom u(z, y) = min(y/=, ,/7)