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The first player can choose either U or D. If he chooses U, the second player has a choice of two strategies: L and R. If the second player moves L he obtains 1 and the first player gets 5. If the second player chooses R he obtains 2 units of payoff while the first player receives 1. Following a move D by the first player, both players engage in a simultaneous-move “Bach or Stravinsky” game (as it was described in class). Find the SPE of this game and write it down in a mixed and behavior form.
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- Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1. At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. For player 2, A stands for Accommodate and F stands for Fight. Player 1 Enter Player 2 A F A Stay out Player 2 F (16,30) (-6,18) In the Nash equilibrium of this game, player 2 earns Player 2 player 1 would play (0,40) (0,20) ✓an incentive to threaten F because, if player 1 believed him then so that player 2 would earn ✓. However, this threat isCandie's Chocolates and Kara's Confections are competing candy stores. Both of them are thinking about opening a store in the town of Economicville. If Kara's opens a store in Economicville and Candie's determines that it is not profitable to also open a store, then Group of answer choices: a Nash equilibrium is not possible in this game. this is a zero-sum game. this is a simultaneous game. Kara's had a first-mover advantage in this game.The centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. In other words, player 1 chooses between D (Down) and A (Across), where D is pocketing the pot and A is passing the pot to the player 2. Similarly, player 2 chooses between A and D. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot on the next round, one receives slightly less than if one had taken the pot on this round. A 2 A A 2 A 1 A (3,5) Ꭰ D D D D (1,0) (0,2) (3,1) (2,4) (4,3) 1. Find the subgame perfect Nash Equilibrium using backward induction.
- The strategies and payoffs are given in the table. The first number of each payoff pair in the matrix is the payoff of player P1, and the second is the payoff of player P2. P2 Strategies Left Right P1 Up (2, 4) (1, 3) Strategies Down (1, 6) (6, 5) Select each pair of actions that would be a Nash Equilibrium of the above game. Up, Left Down, Left Up, Right Down, RightProvide an example of a 2-player normal form game where each player has 3 (pure) strategies such that: (i) There is no pure strategy Nash equilibrium.Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
- (A) Two California teenagers Bill and Ted are playing Chicken. Bill drives his hot rod south down a one-lane road, and Ted drives his hot rod north along the same road. Each has two strategies: Stay or Swerve. If one player chooses Swerve he loses face; if both swerve, they both lose face. However, if they both choose Stay, they are both killed. The payoffs for the game of Chicken are given in the table below. Bill is the row player and Ted is the column player. Stay Swerve Stay -3, -3 2, 0 Swerve 0, 2 1, 1 (i) Find all pure strategy Nash equilibria. (ii) Find the mixed strategy Nash equilibrium. (iii) What is the probability that both teenagers will survive? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.PleaseFind all of the Nash equilibrium of the following three player game. Player 1 chooses rows (a,b). Player 2 chooses columns (c,d). Player 3 chooses matrices (x.y). Player 3 receives the third listed payoff for cach outcome. 5,5,5 4,4,0 8,8,3 7,7,3 1,3,1 4,2,0 3,2,4 3,1,0 a by A) (b,d.x) and (a,d.y) B) (b.cy) OC) (b,d,x) D) (a,d,x) and (b,c.y) E) (b,c,x) OF) (a,d.x)
- Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry's payoff is the fiırst number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [ Select ] v and Kerry will [ [ Select ]Suppose that two firms, firm A and firm B, are competing in the market. Assume that each firm has two strategies available: “no promotion” and “extensive promotion”. If both firms choose “no promotion”, each firm will get a payoff of 8000. If both firms choose “extensive promotion”, each firm will get a payoff of 5000. If one firm chooses “no promotion” and the other firm chooses “extensive promotion”, the firm that chooses “no promotion” will get a payoff of 4000 and the firm that chooses “extensive promotion” will get a payoff of 10000.a. Assume the game is a 2-players one-shot simultaneous game, please develop the normal form of this game by showing the players, the strategies and the payoffs. b. Follow part (a), determine the dominant strategy of firm A. c. Follow part (a), determine the dominant strategy of firm B. d. Follow part (a), determine the equilibrium of this game. e. If the game becomes an infinitely repeated game, what do you expect to happen?Big Pig and Little Pig have two possible strategies each: Press and Wait. Their payoffs for playing each strategy are as follows. Little Pig Press Wait Press 8,2 2,1 Big Pig Wait 10,0 3,3 Which of the following is TRUE? Little Pig will get a payoff of 2 and Big Pig will get a payoff of 8. Little pig will get a payoff of zero. Neither pig has a dominant strategy. Both pigs will wait at the trough.
