Games in Extensive Form: Sequential Decision Making
4.1 Introduction to Game Tree—Gambit
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.
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
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.
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
Since the players make their choices simultaneously, the information set 2 : 1 reflects that player II makes her choice without ...
Get Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.