Bill and Tom are playing a game. At each round of the game, they have to choose either Strategy X or Strategy Y. However, Tom can make a decision only after Bill has made his decision. If they both choose X, each gains $100, and if both of them choose Y, each gains $50. However, if Bill chooses X and Tom chooses Y, Bill gains $60 while Tom gains $140. Similarly, when Bill chooses Y and Tom chooses X, Tom gains $60 while Bill gains $140.
a) Draw a game tree to represent this game.
b) What type of game is being played? What is the procedure used to solve such a game?
c) What is Tom?s optimal strategy if Bill chooses Strategy X?
d) What is Bill?s payoff in equilibrium?

Question

Quizplus · Accepted Answer

The Answer of Bill and Tom are playing a game. At each round of the game, they have to choose either Strategy X or Strategy Y. However, Tom can make a decision only after Bill has made his decision. If they both choose X, each gains $100, and if both of them choose Y, each gains $50. However, if Bill chooses X and Tom chooses Y, Bill gains $60 while Tom gains $140. Similarly, when Bill chooses Y and Tom chooses X, Tom gains $60 while Bill gains $140.
a) Draw a game tree to represent this game.
b) What type of game is being played? What is the procedure used to solve such a game?
c) What is Tom?s optimal strategy if Bill chooses Strategy X?
d) What is Bill?s payoff in equilibrium?

Bill and Tom Are Playing a Game