Reference no: EM132529366 , Length: 3 pages
Problem 1. Consider the following two player game.
(1) Find all the pure strategy equilibria for this game.
(2) Draw a simplex representing the mixed strategy space of Player 1 and carefully mark on it the regions where the three pure strategies of Player 2 are best, explaining how you found these regions and explicitly calculating the extreme points of the various regions.
(3) Draw a simplex representing the mixed strategy space of Player 2 and carefully mark on it the regions where the three pure strategies of Player 1 are best, explicitly calculating the extreme points of the various regions.
(4) Use the two diagrams that you have drawn to find all the mixed equilibria of this game.
Problem 2. Consider the following extensive form game.
(1) List all the pure strategies of each player.
(2) Find all the subgames of the original game.
(3) Find all the subgame perfect equilibria of this game, including any in which the players might play both actions with strictly positive probability at some information sets.
(4) Find the associated normal form of this game. If there are pure strategies that are Kuhn-equivalent, keep only one representative pure strategy for each set of equivalent strategies. Find all the pure strategy Nash equilibria of this game and say which are equivalent to subgame perfect equilibria and which of the subgame perfect equilibria you found in part (2) that each is equivalent to.
(5) Repeat part (4) for the mixed strategy equilibria.
Attachment:- Assignment.rar
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