1. Draw the extensive form (tree) of the following game. 2. Find the perfect equilibrium. What are the payoffs in this equilibrium? 3. Draw the strategic form (matrix) of the game and find a non- perfect equilibrium. Player I chooses "black" or "white". After hearing player I's announcement, Player II also chooses "black" or "white". If both choose "black" - the game ends, and each receives 1. If they choose different colors - the player who chooses "white" receives and the player who chooses "black" receives 0. If both choose "white" - they toss a fair coin. If the outcome is heads-player I receives 4 and player II receives (-2). If the outcome is tails - player II receives 4 and player I receives (-2).

1. Draw the extensive form (tree) of the following game. 2. Find the perfect equilibrium. What are the payoffs in this equilibrium? 3. Draw the strategic form (matrix) of the game and find a non- perfect equilibrium. Player I chooses "black" or "white". After hearing player I's announcement, Player II also chooses "black" or "white". If both choose "black" - the game ends, and each receives 1. If they choose different colors - the player who chooses "white" receives and the player who chooses "black" receives 0. If both choose "white" - they toss a fair coin. If the outcome is heads-player I receives 4 and player II receives (-2). If the outcome is tails - player II receives 4 and player I receives (-2).

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

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Question 1 Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). 1. Determine the range of values for x such that Player 2 has a strictly dominant strategy.
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Question 1 Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). A) Suppose that the value of x is such that player 2 has a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game? B) Suppose that the value of x is such the player 2 does NOT have a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game?
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