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- Which player (if any) has a dominate strategy? What is the Nash Equilibrium of this game? Does the game satisfy the definition of prisoner dilemma?The following payoff matrix represents a simultaneous-move game between two players: John and Trevor. Each player has to choices: Black or White. The first number in each cell is the payoff to John, and the second number is the payoff to Trevor. Trevor Black White Black 15, 15 10, 10 John White 12, 10 13, 15 Refer to the table above. Which statement is true? a. Neither John nor Trevor have a dominant strategy in this game. b. Only Trevor has a dominant strategy in this game. c. Only John has a dominant strategy in this game. d. John and Trevor both have a dominant strategy in this game.Question 3: Represent Rock-Paper-Scissors 1 point, the loser gets -1 and in case of a tie each player gets 0. What are the dominant strategies? What is the Nash equilibrium? game in a matrix format. Note that the winner gets
- Suppose there are two farmers, each of whom has the right to graze cows on the village common. Denote by sA and sB the number of cows farmers A and B graze, respectively. The payoff per cow is given by 120-sA-sB and farmers decide on the number of cows they will graze on the common simultaneously (a) Formulate this situation as a strategic game and find the Nash equilibrium (b) Compare the equilibrium farmer profits to those that would have been realized if each farmer grazed 30 cows on the village common. ExplainUse the following normal-form game to answer the following questions. a. For what values of x is strategy D (strictly) dominant for player 2? b. For what values of x is strategy B (strictly) dominant for player 1? c. For what values of x is (B, D) the only Nash equilibrium of the game?Three married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…
- In a game of chicken, two drivers are heading towards each other on a collision course. The first one to swerve is considered the "chicken" and loses. What is the Nash equilibrium in this game? a) Both drivers swerve b) Neither driver swerves c) One driver swerves while the other doesn't d) It depends on the specificChris Evans Party Don't Party Paparazzo Stalk 3,4 1,1 Don't Stalk 4,2 1,2 Suppose a sequential game in which Paparazzo moves first. What is the subgame perfect Nash equilibrium? (Stalk; Party if Paparazzo chooses Stalk, and Party if Paparazzo chooses Don't Stalk). (Stalk; Party if Paparazzo chooses Stalk, and Don't Party if Paparazzo chooses Don't Stalk). O (Don't Stalk; Party if Paparazzo chooses Stalk, and Party if Paparazzo chooses Don't Stalk). (Don't Stalk; Party if Paparazzo chooses Stalk, and Don't Party if Paparazzo chooses Don't Stalk).In the following two-user game, the payoffs of users Alice and Bob are exactly negative of each other in all the combinations of strategies (a,a), (a,b), (b,a), (b,b). This models an extreme case of competition, and is called a zero-sum game. Please point out every pure-strategy Nash equilibrium of this game, and explain why it is. a b a (1, -1) (3, -3) (2, -2) (5, -5)
- Consider the following payoff matrix below. Player 1 and Player 2 have two options, A or B. The payoffs are given in the form of (Player 1, Player 2). Higher numbers are more desirable. What is Player 2's dominant strategy? Player 2 B A Player 1 A 5,6 2,2 B 4,3 5,2 O Play A Play B O No Dominant StrategyHello, please help me to solve this Game Theory question. Thanks in advance! Hobby hunter Jack decides what to do the next weekend. He can either stay at home and watch movies (Movies), or call his friend Katherine to go hunting (Hunt). If he stays in, both Jack and Katherine get a payoff of 2. If he decides to hunt, he knows the situation with his friend will resemble a classic stag hunt game with simultaneous moves: Hunting a stag is better than hunting a rabbit, but it only works if they cooperate. The hunting subgame is captured as: Katherine Stag Rabbit Jack Stag 3 , 3 0 , 1 Rabbit 1 , 0 1 , 1 Are the Nash Equilibria of the full game credible?Comment on any Nash equilibria of the full game which are not credible.Find all subgame perfect equilibria in pure strategies.Hello, please help me to solve this Game Theory question. Thanks in advance! Hobby hunter Jack decides what to do the next weekend. He can either stay at home and watch movies (Movies), or call his friend Katherine to go hunting (Hunt). If he stays in, both Jack and Katherine get a payoff of 2. If he decides to hunt, he knows the situation with his friend will resemble a classic stag hunt game with simultaneous moves: Hunting a stag is better than hunting a rabbit, but it only works if they cooperate. The hunting subgame is captured as: Katherine Stag Rabbit Jack Stag 3 , 3 0 , 1 Rabbit 1 , 0 1 , 1 1. Write the normal form representation of the full game, including Jack’s initial decision.2. Identify any pure-strategy Nash equilibria. How does this compare to the pure strategy Nash equilibria of the hunting game alone?