a) In the game Matching Pennies, two players with pennies simultaneously choose whether to play Heads or Tails. If the two pennies match (HH or TT), then Player 1 wins. If the two pennies don't match (HT or TH), then Player 2 wins. This is essentially the same as what happens when someone serves in a game of tennis. Try to find all of the Nash Equilibria in the game shown below. Payoffs are listed in terms of profits to Venus (TV) and to Serena (Ts). Serena's Return Choice Forehand Backhand Forehand ITy = -1, As = 1 ITy = 1, As = -1 Venus' Service Choice Backhand JTy = 1, Ts = -1 ITy = -1, As =1

a) In the game Matching Pennies, two players with pennies simultaneously choose whether to play Heads or Tails. If the two pennies match (HH or TT), then Player 1 wins. If the two pennies don't match (HT or TH), then Player 2 wins. This is essentially the same as what happens when someone serves in a game of tennis. Try to find all of the Nash Equilibria in the game shown below. Payoffs are listed in terms of profits to Venus (TV) and to Serena (Ts). Serena's Return Choice Forehand Backhand Forehand ITy = -1, As = 1 ITy = 1, As = -1 Venus' Service Choice Backhand JTy = 1, Ts = -1 ITy = -1, As =1

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 15.1IP

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Sam and Sarah are thinking about getting married. However if either of them cheats on the other, they would get a payoff of 10, while the other person gets zero. If neither cheat, they stay with each other and get a payoff of 7 each and if both cheat, the relationship falls apart and each get a payoff of 1. What is the Nash equilibrium of this game? a. Cheat, Cheat b. Not cheat, Not cheat Sam cheats, Sarah doesn't Sarah cheats, Sam doesn't
i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.
Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 ہے A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.
. In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. a. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. b. Is there a pure strategy? Why or why not? c. Determine the optimal strategies and the value of this game. Does the game favor one player over the other? d. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
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Game Theory and Strategic Choices – End of Chapter Problem The Old Familiar and The Beehive are the only two bistros in town. Each is trying to decide whether or not it should advertise in the local newspaper. The accompanying payoff table gives their weekly profits under each possible outcome. The Beehive The Beehive does advertise does not advertise The Old Familiar The Old Familiar earns $X in profits. earns $3,500 in profits. The Old Familiar does advertise The Beehive The Beehive earns $Y in profits. earns $2,250 in profits. The Old Familiar The Old Familiar earns $2,000 in profits. earns $2,500 in profits. The Old Familiar does not advertise The Beehive The Beehive earns $4,000 in profits. earns $3,500 in profits. a. Which combination or combinations of X and Y would make a situation in which The Old Familiar does not advertise and The Beehive advertises a Nash equilibrium?
Question 2 The game of Chicken is played by two teens who speed toward each other on a single lane road. The first to veer off is branded the chicken, whereas the one who doesn’t veer gains peer- group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the Chicken game are provided in the following table. TEEN 2 TEEN 1 Veer Don't Veer Veer Don't Veer 2,2 3,1 1,3 0,0 a) Draw the extensive form. b) Find the pure-strategy Nash equilibrium or equilibria. c) Compute the mixed-strategy Nash equilibrium. As part of your answer draw the best- response function diagram for the mixed strategies. d) Suppose the game is played sequentially with teen A moving first and committing to this action by throwing away the steering wheel. What are teen B's contingent strategies? Write down the normal and extensive forms for the sequential version of the game. e) Using the normal form for the sequential version of the game, solve for the Nash equilibria. f) Identify the proper…
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