4. Finding Nash equilibria in sequential gamesHubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to seeone movie (call it movie H) and Larry would prefer to see the other movie (movie L), but both would prefer to see one of the movies together ratherthan their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power, cutting the conversation short. Bothmovies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The followingpayoff matrix represents the game they are playing.HubertMovie HMovie LHubertLarryMovie H45, 300,0Suppose Larry is near home and quickly starts charging his phone. At home, however, he gets terrible phone service but a strong wireless signal.Therefore, instead of calling Hubert, he uses a smartphone app to observe Hubert's location using GPS. Because Larry can see whether Hubert headsin the direction of movie H or movie L, he can base his decision on Hubert's decision. Hubert's phone alerts him that Larry is tracking him.Movie HMovie LHubert still has the same strategies available, but Larry now has four possible strategies. The following table represents the sequential version of thisgame in normal form. The table shows each strategy as the letter for the movie Larry chooses, followed by a vertical bar, followed by the letter for thecorresponding movie Hubert chose.Movie L0,030, 45Strategy 1LIH; LILLarryStrategy 2H|H; H|LStrategy 3H|H; LILStrategy 4LIH; HILIf Larry decides to choose movie L conditional on Hubert's choosing movie H and L conditional on Hubert's choosing movie L (that is, he chooses toalways go to movie L), he is playingComplete the previous table by choosing the correct payoffs according to each of the strategies that Larry chooses and the actions Hubert chooses.Hubert's payoff is given first, as in the preceding payoff matrix.Which of the following represent a Nash equilibrium in this sequential version of the game? Check all that apply.Hubert goes to movie H and Larry plays strategy 2Hubert goes to movie L and Larry plays strategy 1Hubert goes to movie H and Larry plays strategy 1Hubert goes to movie L and Larry plays strategy 3Hubert goes to movie H and Larry plays strategy 3

There are two players : Hubert & Larry Strategy Set of Hubert = Strategy Set of Larry = { Movie…

Hubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to see one movie (call it movie H) and Larry would prefer to see the other movie (movie L), but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power, cutting the conversation short. Both movies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The following payoff matrix represents the game they are playing. Larry Movie H Movie L

Hubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to see one movie (call it movie H) and Larry would prefer to see the other movie (movie L), but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power, cutting the conversation short. Both movies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The following payoff matrix represents the game they are playing. Larry Movie H Movie L

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 3MC

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. Arif and Aisha agree to meet for a date at a local dance club next week. In their enthusiasm, they forget to agree which venue will be the site of their meeting. Luckily the town has only two dancing venues, Palms and Oasis. Having discussed their tastes in dancing venues last week, both know that Arif prefers Palms to the Oasis and Aisha prefers the Oasis to Palms. In fact, their payoffs reflect that if both go to Oasis, Aisha’s utility is 3 and Arif’s 2, while if both go to Palms Arif’s utility is 3 and Aisha’s is 2. If they do not go to the same venue, then they both have a utility of 0Please calculate mixed strategy equilibria, if any, and then derive the probability that Arif and Aisha will find themselves at the same venue.
8. Solving for dominant strategies and the Nash equilibrium Suppose Tim and Alyssa are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Tim chooses Right and Alyssa chooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6. Tim Left Left 5, 6 Right 4, 2 Alyssa Right 5,5 3,6 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Tim chooses and Alyssa chooses
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3. Solving for dominant strategies and the Nash equilibrium Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 3 and Dina will receive a payoff of 8. Dina Left Right Left 3,7 2,6 Charles Right 4,5 3,8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses
2) There are two cola companies, Pepsi and Coke, that each own a vending machine in the dormitory. Each must decide how to stock its machine. They can fill the machine with diet soda, regular soda, or a combination of the two. The payoffs are in the strategic form of the game presented below. Соса-Cola Diet Both Classic Diet 25, 25 50, 30 50, 20 Реpsi Both 30, 50 15, 15 30, 20 Classic 20, 50 20, 30 10, 10 (a) What strategies survive iterated elimination of strictly dominated strategies? (b) What are the pure-strategy Nash equilibria?
2. Consider the following game. Two criminals are thinking about pulling off a bank robbery. The take from the bank would be $20,000 each, but the job requires two people (one to rob the bank and one to drive the getaway car. Each criminal could instead rob a liquor store. The take from robing a liquor store is only $1000 but can be done with one person acting alone. Write the payoff matrix of this game Player A Bank job Liqour store Player B Bank job Liquor store a. What are the Nash equilibria in this game? b. Explain why there can be multiple equilibria in this game. c. How the game will be played if mixed strategies are allowed? Discuss.
5. Aaron and Betty play the following one-shot game. Aaron Up Middle Down Left 10,0 5,10 1,1 Betty Right 0,5 1,0 2,2 a. Does the game above have any (pure strategy) Nash equilibria? Find any equilibria or explain why an equilibrium doesn't exist. b. Suppose instead that Aaron moves first and Betty moves second. Represent this situation with a game tree and find the subgame perfect Nash equilibrium. Are Aaron and Betty better off playing a simultaneous game or a sequential game in which Aaron moves first? Explain. c.
2. In the following game, players must move simultaneously. How many Nash equilibria are there? Which will occur without collusion? Which will occur if collusion is allowed? (Collusion means if they make contract to identify firms’ strategy before game is played.) Firm 2 A В A 3, 1 7,0 Firm 1 В 2, 4 5, 3
7. Solving for dominant strategies and the Nash equilibrium Suppose Dmitri and Frances are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Dmitri chooses Right and Frances chooses Right, Dmitri will receive a payoff of 7 and Frances will receive a payoff of 6. Frances Left Right Left 4, 3 6, 4 Dmitri Right 6, 7 7, 6 to choose The only dominant strategy in this game is for and Frances chooses The outcome reflecting the unique Nash equilibrium in this game is as follows: Dmitri chooses v
4. Consider the two-player Rock-Paper-Scissors game. Each player can choose between three pure strategies: Rock, Paper, and Scissors. Strategy Rock beats Scissors, but loses to Paper. Strategy Paper beats Rock but loses to Scissors. Strategy Scissors beats Paper, but loses to Rock. When the game is a draw, the payoff for the players is '0'. The payoff of winning is ‘+1' and the payoff of losing is '-1'. Formulate this problem as a two-person, zero-sum game by constructing a payoff table.
1. Each of two players simultaneously announces either Rock, Paper, or Scissors. Paper beats Rock, Rock beats Scissors, and Scissors beats Paper. The player who names the winning object receives $1 from her opponent. If both players make the same choice, no payment is made. Each players's preferences are represented by by the expected amount of money she receives. a) Formulate the situation as a strategic game and find all its mixed strategy equilibria. Make sure that you consider all different supports. b) Find all the mixed strategy equilibria of the modified game in which player 2 is prohibited from announcing Rock.
9.