1. Consider the following Prisoner's Dilemma Game:CDC2,20,3D3,01,1Calculate the values of 8 (if any) to achieve a subgame perfect equilibrium in theinfinitely repeated game, with the following Pavlov strategy for both players:1. To Choose C in period 12. To choose C after any history where the action chosen in the last period wereeither (C,C) or (D,D).3. To choose D after any other history.Repeat the above analysis for the PD game with payoff matrix:CDC4,40,6D6,01,1

The objective of the question is to find the values of discount factor (δ) that would make the…

Answered: 1. Consider the following Prisoner's…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.6P

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1. Consider the following two player 2x2, normal form game: (Payoffs are starting from northwest and moving clockwise are (10,5), (2,30), (5,5), and (40,10). Player 1 strategies are A and B, Player 2 strategies are C and D. Identify all Nash equilibria in pure strategies. a) 2. Using the normal form game, represent a two-player Rock-Paper-Scissors-Game where Player 1's losses and gains are triple that of Player 2.
2. Consider the following 2 → 2 normal form games: In both games Player 1 (the row player) chooses either strategy A or strategy B. Player 2 (the column player) chooses simultaneously strategy A or B. The outcomes are defined by the following matrices. The first number in each cell indicates the payoff of Player 1, the second number (after the comma) indicates the payoff of Player 2. A B Game I A B 50X, 30X 10X, 10X 10X, 10X 30X, 50X Game II A A 110X, 30X B 10X, 10X B 10X, 10X 30X, 50X where X > 0 is a payoff scale parameter. (a) For both games: find all Nash equilibria in pure strategies, if any, and find the Nash equilibrium in mixed strategies. How would you describe this strategic interaction in the two games?
Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.
1. Consider the following normal form game: Player 2 Player 1 U (2,2) (1,6) Find the mixed-strategy Nash equilibrium, supposing that this is a simultaneous non- repeated game.
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…
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.
Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana Inc. 400 70 300 Strategy B 40 80 100 90 150 80 Strategy C
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)
Make sure you clearly write your name and submission:. 1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. • "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper -1 0 1 rock 0 paper 1 scissors -1 (a) Show that this game does not have a pure Nash equilibrium. 1 X 3 (b) Show that…
Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 50, 50 -110, 6 B 6, -110 26, 26 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.check all that apply (26,26) (50,50) (-110,6) (6,-110) Which of these outcomes would you consider most likely?multiple choice 1 (-110,6) (50,50) (6,-110) (26,26) b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?multiple choice 2 B A What outcome do you think would occur as a result?multiple choice 3 (26,26) (50,50) (-110,6) (6,-110) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move…
Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 30, 30 16, -50 B -50, 16 50, 50 A. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. check all that apply (16, −50) (−50, 16) (30, 30) (50, 50) Which of these outcomes would you consider most likely? multiple choice (16, −50) (50, 50) (−50, 16) (30, 30) B. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter? multiple choice A or B What outcome do you think would occur as a result? multiple choice (−50, 16) (16, −50) (30, 30) (50, 50) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is…

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