Two players, Player 1 and Player 2, are playing a repeated prisoner's dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Player 2 A B Player 1 A 10,10 1,150 B 150, 1 2,2 Select one:
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- Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Suppose player 1 plays a mixed strategy in which she plays U 25% of the time and D 75% of the time, and player 2 plays a mixed strategy in which she plays L 25% of the time and R 75% of the time. This pair of strategies ✓a Nash equilibrium. Player 1's expected payoff from playing U (when player 2 plays the mixed strategy above) isConsider 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 2Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.
- Q2 Consider a game between 2 payers (Ann and Bill) where each chooses between 3 actions (Up, Middle and Down). 1) Create a payoff matrix that reflects this. 2) Fill in payoff numbers that makes this game a Prisoner's Dilemma. 3) Explain why your game is a Prisoner's Dilemma.Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals: (a) $3 for the first mover and $1 for the second mover, (b) $2 for each, or (c) $1 for the first movier and $3 for the second mover. The second mover is shown the proposal and can either accept, in which case it is implemented, or reject and cause each to earn $0. Show this game in extensive (tree) form. Be sure to show the payoffs for each person, with the first mover listed on the left, for each of the six terminal nodes.
- Consider the following centipede game consisting of two players, Pl and P2. The left/right number each terminal node represents Pl's/P2's payoff, respectively. Then, answer the following questions of [D5] and [M5]-|M8]: P1 G P2 P1 G -(0, 2) D (2, 0) (1, 1) (4, 0) Suppose that P2 chooses G or D randomly. Then, what is the Pl's best response of P1 for the P2's choice? And explain why. We assume that random choice is level-0 in the level-k theory. Then, answer the P2's choice in level-2. (a) D (b) G (c) random choice on (G, D) (d) G with probability 1/3 Answer all the properties of Nash equilibrium and subgame perfect equilibrium which is derives from the backward induction. (a) All subgame perfect equilibria are Nash equilibria in any game. (b) All Nash equilibria are subgame perfect equilibria in any game. (c) There is always a unique Nash equilibrium in any game. (d) There exist pure-strategy Nash equilibria in any game. (e) The Nash equilibrium in prisoners' dilemma game is socially…3. Two individuals are planning to start a business. The earnings from a grocery store business would be $30,000 for each, but the business requires two people (one to watch over the stock and the other to act as a cashier). Each individual could instead start an mpesa business. The take from mpesa business is only $3000 but can be done with one person acting alone. i) Write down the payoff matrix for this game ( ii) Solve the Nash equilibriumKeith and Blake play a simultaneous one-shot game given by the following table: Blake Left Right Keith Top Bottom 4.00, -5.00 0.00, -6.00 5.00, 0.00 -2.00, 7.00 As there is no unique pure strategy Nash equilibrium, assume that each player plays each of his choices half of the time. What is the average payoff for Keith? | What is the average payoff for Blake? (Round to two decimals if necessary.) (Round to two decimals if necessary.)
- 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 ]a) Draw an extensive form game with 4 outcomes (2 moves for player 1 followed by 2 moves for 2 after each of 1's moves) and no pure strategy Nash equilibrium. b) Write the strategic form to verify your answer to (a) c) Draw an extensive form 2-player game, in which both players always move, that has exactly 4 outcomes, 1 subgame perfect Nash equilibrium and no non-subgame perfect Nash equilibrium and no dominant strategies. d) Write the strategic form and use it to verify your answer to (b)Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits to her choice of effort level first. On observing this decision, Nancy commits to her own effort level. What is the subgame - perfect equilibrium of the game where the joint profits are 5m + 4n+ mn, the costs of their efforts to Monica and Nancy are m2 and n2, respectively, and Monica commits to an effort level first? Compare the payoffs to Monica and Nancy with those found in Exercise U10 in Chapter 5. Does this game have a first-mover or second - mover advantage? Using the same joint profit function as in part (a), find the subgame - perfect equilibrium for the game where Nancy must commit first to an effort level. U10. Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits…
