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Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition by E. N. Barron

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Games in Extensive Form: Sequential Decision Making

4.1 Introduction to Game Tree—Gambit

Problems

4.1 Convert the following extensive form game to a strategic form game. Be sure to list all of the pure strategies for each player and then use the matrix to find the Nash equilibrium.

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4.1 Answer: Player I has two pure strategies: 1 = take action 1 at node 1 : 1, and 2 = take action 2 at node 1 : 1. Player II has three pure strategies: 1 = take action 1 at information set 2 : 1, 2 = take action 2 at 2 : 1, and 3 = take action 3 at 2 : 1.

The game matrix is

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There is a pure Nash at (4, 1).

4.2 Given the game matrix draw the tree. Assume the players make their choices simultaneously. Solve the game.

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4.2 Answer: The solution of the matrix game is the Nash equilibrium at row 2, column 1, giving payoffs (4, 0). The equivalent tree form of the game is

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Matrix to tree.

Since the players make their choices simultaneously, the information set 2 : 1 reflects that player II makes her choice without ...

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