! 1Solve the game with the given payoff matrix.-6 -12 02.0 1P =1 00 -2 2Optimal row player strategyO There are infinitely many optimal row strategies, obtained by taking linear combinations of 2/5 3/5 0 0and1/3 2/3 0O There are infinitely many optimal row strategies, obtained by taking linear combinations of[000 1] and 1/3 2/30 0[1/3 2/3 0 0].[1000].O There are infinitely many optimal row strategies, obtained by taking linear combinations of 2/5 8/15 0 1/15 andO There are infinitely many optimal row strategies, obtained by taking linear combinations of 2/5 8/15 0 1/15 andThere are infinitely many optimal row strategies, obtained by taking linear combinations of 2/5 8/15 0 1/15 and2/5 3/5 0 0Optimal column player strategyExpected value of the game

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Answered: O T9 O N 1OH O Solve the game with the…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.6P

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Economics Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first): · (250, 290) if both firms deviate · (290, 330) if both firms cooperate · (230, 370) if only firm 2 deviates · (350, 270) if only firm 1 deviates a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated? b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?
Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibrium
if Y = 4 (a) If ⟨a,d⟩ is played in the first period and ⟨b,e⟩ is played in the second period, what is the resulting (repeated game) payoff for the row player? (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?
Q14. Do players have perfect information in the above game? Yes, all of them have perfect information No, player 2 has imperfect information No, player 3 has imperfect information No, no player has perfect information Q15. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players be? Player 1={a, b, c} ; Player 2={x, y}; Player 3={r, s} Player 1={a, b, c} ; Player 2={xx, xy, yx, yy}; Player 3={r, s}
Suppose that 5 risk neutral competitors participate in a rent seeking game with a fixed prize of $100. Each player may invest as much as he wishes in the political contest, although those investments have an opportunity cost equal 1. The probability of winning is directly proportional to the candidate’s share of the total rent-seeking investment. What is the profit-maximizing investment by player 1 as a function of the investment by all the others? What is a Nash equilibrium investment by each player in a symmetric game?
Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.
Consider the following two person game. Player 1 begins the game by choosing A or B. If Player 1 chooses A the game ends and Player 1 receives $100 and Player 2 receives $100. If Player 1 chooses B then Player 2 must choose C or D. If Player 2 chooses C then Player 1 receives $150 and Player 2 receives $250. If Player 2 chooses D then Player 1 receives $0 and Player 2 receives $400. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Using backwards induction (look forward and reason backwards) determine the rational outcome to this game. Given how experimental subjects have behaved in the Ultimatum game, provide a behavioral explanation for why an “average” Player 1 and 2 might deviate from the rational prediction.
Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?
Consider the following strategic game with 2 players: P1 AND P2 E F G H A 10,30 0,50 5,5 40,20 B 40,10 10,10 8,20 30,5 C 15,5 10,30 5,20 25,20 D 20,3 20,8 6,6 20,0 (a) Specify the strategies for P1 and P2, respectively. Eliminate all strictlydominated strategies, and FIND the reduced game until you can reduce the game nofurther.(b) Find all the Nash equilibria for the reduced game, including the mixed-strategy ones

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