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…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Refer to Table Left-Right-ZigZag. How many pure strategy Nash equilibria does this game have? Table: Left-Right-ZigZag Player 1 Drive left Driver right Zigzag 1) 1 2) 2 3) 3 4) 4 5) None of the above. Drive left (1,1) (-1,-1) (0,0) Player 2 Driver right (-1,-1) (1,1) (0,0) Zigzag (0,0) (0,0) (0,0)
PART C D
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Two firms are competing to establish one of two new wireless communication standards, A or B. A strategy is a choice of standard, and an outcome of this game is a choice of standard by each firm – for example, (A, B) represents the case where Firm 1 decides to develop standard A and Firm 2 develops standard B. Here, the first letter will always correspond to Firm 1’s decision, and the second letter to Firm 2’s decision. Firm 1 has the following preferences over outcomes, in order of highest to lowest preferred: it prefers (A, A) to (B, A) to (A, B) to (B, B). Firm 2 prefers (A, B) to (A, A) to (B, A) to (B, B). Suppose that firms simultaneously decide which standard to develop. What is the pure strategy Nash equilibrium?
Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.
Up Down Up Up Down Down Player 1 Player 2 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95
Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is CORRECT? Player #1 Player #2 Top Bottom Left 7.7 4.0 Right 0,4 4,4 O There are three equilibria in this game: two pure strategy equilibria at [Top, Left] and [Bottom, Right) and al third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game. Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. O There are three equilibria in this game; two pure strategy equilibria at (Top. Left) and (Bottom, Right) and a third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability and %. O There is a unique dominant…
Player 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.
Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any dominated strategies in this game. If there are none, state this clearly.
Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.
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 scissors rock 0 -1 1 paper 1 0 scissors -1 1 -1 0 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper…

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