What is the subgame perfect equilibrium of this game 4 Suppose that 2 players i

# What is the subgame perfect equilibrium of this game

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adds up to at least 6. What is the subgame perfect equilibrium of this game?4. Suppose that 2 players,i{1,2}, are playing a sequential, perfect information, version ofa modified “Battle of the Sexes” game. Player 1 choosesBorOfirst, after which player 2choosesBorOafter observing player 1’s choice. The payoffs from the terminal nodes aregiven as follows (with the first entry of each payoff vector representing player 1’s payoffand the second representing player 2s payoff):BOB(2,1)(-4,0)O(0,0)(1,2)(a) Draw this as an extensive form game.(b) Find a subgame perfect Nash equilibrium of this game.(c) Find a Nash equilibrium of this game that is not subgame perfect.5. Consider the following 3 player game. Player 1 names a numberx1[1,10], after whichplayer 2 observesx1and names a numberx2[1,10]. Finally, player 3 observesx1andx2and names a numberx3[1,10]. 1
(a) Draw this as an extensive form game (obviously, without payoffs).(b) Suppose that the player who names the number closest to 0.25(x1+x2+x3)receivesa payoff of 1 and each of the other players receives a payoff of 0. (If two or more playerstie for the prize, they split it equally.) Find a subgame perfect Nash equilibrium ofthis game.

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• Spring '11