=a) Suppose x 4 and y = 3. After all strategies that are dominated by a purestrategy are iteratively deleted for both players, how many strategies remain forPlayer 1?b) Suppose x = 4 and y = 3. After all strategies that are dominated by a purestrategy are iteratively deleted for both players, how many strategies remain forPlayer 2?c) Suppose x = 4 and y = 3. What is the sum of both players' payoffs in all purestrategy Nash equilibria of the game?d) Suppose x = 4 and y = 11. After all strategies that are dominated by a purestrategy are iteratively deleted for both players, how many strategies remain forPlayer 1?e) Suppose x = 4 and y = 11. After all strategies that are dominated by a purestrategy are iteratively deleted for both players, how many strategies remain forPlayer 2?f) Suppose x = 4 and y = 11. What is the sum of both players' payoffs in all purestrategy Nash equilibria of the game?

(e) Suppose x=4 and y=11. After all strategies that are dominated by a pure strategy are iteratively…

Answered: = a) Suppose x 4 and y = 3. After all…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Does this game have an iterated dominance equilibrium? Find the best responses of the players. Find the Nash equilibria of the game. Is a threat by either player not to swerve a credible threat? Why or why not? Would the ability of one player to firmly commit to a no-chicken strategy be desirable for that player?
Consider a three-player game where the strategy of player i is ri ∈ [1,2]. Player 1’s payoff function is V1(r1, r2, r3) = 1 - r1 + 2r2 - 3r3, player 2’s payoff function is V2(r1, r2, r3) = 1 + r1 + 4r2 + 2r3, and player 3’s payoff function is V3(r1, r2, r3) = (3 - r1 - r2)r3. Find all Nash equilibria.
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.
Each of 3 companies are considering entry into a new market. The cost of entry is 30. If only one company enters, then its gross profit is 200. If more than one company enters, then each entrant earns a gross profit of 40. The payoff to a company that enters is its gross profit minus its entry cost, while the payoff to a company that does not enter is 60. This implies that if all companies enter the market their payoffs are 10 while if all of them stays out their payoffs are 60. If only one company enters the market its payoff is 170 (while the other two companies’ payoffs are 60). If two companies enter the market their payoffs are 10. Problem Set 2 Due Sunday October 3rd You can discuss the problem set with your classmates, but you are required to submit your independent answers. a) Find all pure strategy Nash equilibria of the game. b) Can you find a mixed strategy Nash equilibrium such that exactly one company plays mixed strategy? If yes, what is it? c) Can you find a mixed…
Which one of the following descriptions is WRONG, according to this Extensive Form shown below? 1.) There are 8 strategy profiles in this game. 2.) If Player 1 chooses strategy IA and Player 2 chooses strategy O, then player 1's payoff will be 4. 3.) If Player 1 chooses strategy OB and Player 2 chooses strategy I, then Player 2's payoff will be 2. 4.) Game over if Player 1 chooses O initially.
Consider a location game with nine regions like the one discussed in this chapter. But instead of having the customers distributed uniformly across the nine regions, suppose that region 1 has a different number of customers than the other regions. Specifically, suppose that regions 2 though 9 each has ten customers, whereas region 1 has x customers. For what values of x does the strategy of locating in region 2 dominate locating in region 1?
Eliminate strictly dominated strategies. If the game does not have a pure strategy Nash equilibrium, find the mixed strategy Nash equilibrium for the smaller game (after eliminating dominated strategies). Player 2 с Player 1 A 2,4 B 3,3 a) b) a 4,3 1,3 b 3,2 5,3
Alice chooses action a or action b, and her choice is observed by Bob. If Alice chooses action a, then Alice receives a payoff of 5 and Bob receives a payoff of 4. If Alice chooses action b, then Bob chooses action c or action d. If Bob chooses action c, then Alice receives a payoff of 10 and Bob receives a payoff of 5. If Bob chooses action d, then Alice receives a payoff of 0 and Bob receives a payoff of 6. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) Alice's backward induction payoff is 10. This is a prisoners' dilemma. This game has imperfect information. Alice's backward induction payoff is 0. This is a promise game. Bob's backward induction payoff is 4. Bob's backward induction payoff is 6. This is a threat game.
A small community has 10 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $300 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is one half of the total amount of money contributed by all individuals in the community. This game has a Nash equilibrium in which 5 people contribute $300 and for public entertainment and 5 people contribute nothing. This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment. This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies. This game has a dominant strategy equilibrium in which all 10 citizens contribute $300 to support public entertainment. This game has two Nash equilibria, one in which everybody contributes $300 and one in which no- body contributes $300.
Player 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. What is the Nash equilibrium in this game? Strategy 1 and Strategy A Strategy 2 and Strategy A Strategy 2 and Strategy B This game does not have a Nash equilibrium
(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.

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