Bill and Tom Are Playing a Game

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The Answer is a) The game tree for this game is shown below.

a) The game tree for this game is shown below. b) This is an extensive-form game. The procedure that is used to solve this type of game is called backward induction. Backward induction is the procedure of solving an extensive-form game by first considering the last moverʹs decision. c) If Bill chooses Strategy X, Tom will gain $100 by choosing Strategy X while he will gain $140 by choosing Strategy Y. Therefore, Tomʹs optimal strategy is Y if Bill chooses Strategy X. d) Tom will choose Strategy Y if Bill chooses Strategy X because it will give him a higher payoff. Tom will choose Strategy X if Bill chooses Strategy Y because it will give him a higher payoff. Given this information, Bill will choose the strategy that will give him a higher payoff. Therefore, Bill will choose Strategy Y and his payoff will be $140 in equilibrium.

b) This is an extensive-form game. The procedure that is used to solve this type of game is called backward induction. Backward induction is the procedure of solving an extensive-form game by first considering the last moverʹs decision.
c) If Bill chooses Strategy X, Tom will gain $100 by choosing Strategy X while he will gain $140 by choosing Strategy Y. Therefore, Tomʹs optimal strategy is Y if Bill chooses Strategy X.
d) Tom will choose Strategy Y if Bill chooses Strategy X because it will give him a higher payoff. Tom will choose Strategy X if Bill chooses Strategy Y because it will give him a higher payoff. Given this information, Bill will choose the strategy that will give him a higher payoff. Therefore, Bill will choose Strategy Y and his payoff will be $140 in equilibrium.

Bill and Tom Are Playing a Game

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Bill and Tom Are Playing a Game

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Correct Answer:
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