8. Solving for dominant strategies and the Nash equilibriumSuppose Tim and Alyssa are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows showsthe 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 Alyssachooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6.TimLeftLeft5, 6Right 4, 2AlyssaRight5,53,6The only dominant strategy in this game is forto chooseThe outcome reflecting the unique Nash equilibrium in this game is as follows: Tim choosesand Alyssa chooses

In game theory, a situation known as a Nash equilibrium is one in which each player or participant…

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 fo 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 chooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6. Tim Alyssa Left Left 5,6 Right 4, 2 Right 5,5 3,6 The only dominant strategy in this game is for to choose ▶

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 fo 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 chooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6. Tim Alyssa Left Left 5,6 Right 4, 2 Right 5,5 3,6 The only dominant strategy in this game is for to choose ▶

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Consider the two-by-two bimatrix game listed below: Left Right (2,-2) (1,-1) Up Down (3,-3) (-1,1) where the player "Row" chooses the action "up" or "down" and the player "Column" chooses the action "left" or "right". Describe a mixed strategy Nash Equilibrium for this game.
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4. Finding Nash equilibria in sequential games 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. Hubert Movie H Movie L Hubert Larry Movie H 45, 30 0,0 Suppose 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…
3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 8
7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah 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 Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses
7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 6 and Aaliyah will receive a payoff of 4. Russell Up Down Aaliyah Up 6,3 3,3 Down 6,4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses and Aaliyah chooses
For the game in FIGURE 7.6, derive players’ best-reply functions, plot them as shown in Figure 7.5, and find the Nash equilibrium.
Mimi wants to support her son Jeff if he looks for work but not otherwise. Jeff (unlike most young people) wants to try to find a job only if his mother will not support his life of indolence. Mimi and Jeff's payoff matrix is illustrated in the figure to the right. If Jeff and Mimi choose actions simultaneously, what are the pure- or mixed-strategy Nash equilibria? Determine the pure-strategy Nash equilibrium for this game. O A. The Nash equilibrium is for Mimi to support and Jeff to loaf. B. The Nash equilibrium is for Mimi to support and Jeff to look for work. OC. The Nash equilibrium is for Mimi to not support and Jeff to look for work. D. This game has no Nash equilibria. E. The Nash equilibrium is for Mimi to not support and Jeff to loaf. Determine the mixed-strategy Nash equilibrium for this game. The mixed-strategy Nash equilibrium is for Mimi to support with probability 0M = and for Jeff to look for work with probability 0₁ = (Enter your responses rounded to two decimal…
9. For the payoff matrix below, consider a sequential version of the game in which Player 2 moves first and then Player 1 moves second. Which of the following is not a correct statement? Player 1 Top Center Bottom Left 1,2 5,1 6,0 Player 2 Middle 7,1 11,2 -4,3 Right 10,4 1,0 8,5 The subgame perfect payoffs coincide with those of a Nash equilibrium b. Depending on Player 2's move, Player 1 will sometimes optimally choose Bottom c. Player 2 will choose Right in the subgame perfect equilibrium d. Player 2 would be willing to pay a positive $ amount to move first rather than second e. Player 1 would be willing to pay a larger $ amount than Player 2 to move first
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Keith and Blake play a simultaneous one-shot game given by the following table: Blake Left Right Тop 5.00. -5.00 0.00, -6.00 Kelth Bottom 6.00,0.co -2.00, 8.00 As there is no unique pure strategy Nash equilibrium, assume that each player plays each of his chcices half of the time. What is the average payoff for Keith? (Round to two decimals if necessary.) What is the aver age payoff for Blake? |(Round to two decimals if necessary)
Consider the following game. Which one of the following statements is FALSE? 1. There are 7 subgames in this extensive-form game. 2. There are 6 proper subgames in this extensive-form game. 3. (BK, CE) is a Subgame Perfect Nash Equilibrium. 4. (BK, DE) is a Subgame Perfect Nash Equilibrium