Kk.32. Which of the following constitutes a mixed strategy Nash equilibrium of the Odds and Evens game?Firm APlay Even and Odd with 50% probability each.Play Even with 75% probability and Odd with 25% probability.Always play Even.This game has no mixed strategy Nash equilibrium.Do NotEnter0Enter12Enter10Firm B0-2040Do NotEnter500The above figure shows the payoff to two airlines, A and B, of serving a particular route. If the two airlinesmust decide simultaneously, how many pure Nash equilibria are there?0It cannot be determined.0

Nash equilibrium (NE) is a situation in a game where each player chooses their best strategy in…

Which of the following constitutes a mixed strategy Nash equilibrium of the Odds and Evens game? Firm A Play Even and Odd with 50% probability each. Play Even with 75% probability and Odd with 25% probability. Always play Even. This game has no mixed strategy Nash equilibrium. Do Not Enter Enter 0 2 Enter 10 Firm B 0 -20 40 Do Not Enter 50 0 The above figure shows the payoff to two airlines, A and B, of serving a particular route. If the two airlines must decide simultaneously, how many pure Nash equilibria are there? 0 It cannot be determined.

Which of the following constitutes a mixed strategy Nash equilibrium of the Odds and Evens game? Firm A Play Even and Odd with 50% probability each. Play Even with 75% probability and Odd with 25% probability. Always play Even. This game has no mixed strategy Nash equilibrium. Do Not Enter Enter 0 2 Enter 10 Firm B 0 -20 40 Do Not Enter 50 0 The above figure shows the payoff to two airlines, A and B, of serving a particular route. If the two airlines must decide simultaneously, how many pure Nash equilibria are there? 0 It cannot be determined.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.2P

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Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
a) Find the Nash equilibria in the game (in pure and mixed strategies) and the associated payoffs for the players. b) Now assume that the game is extended in the following way: in the beginning Player 1 can decide whether to opt out (this choice is denoted by O) or whether to play the simultaneous-move game in a) (this choice is denoted by G). If Player 1 opts out (plays O) then both Player 1 and Player 2 get a payoff of 4 each and the game ends. If Player 1 decides to play G, then the simultaneous-move game is played. Find the pure-strategy Nash equilibria in this extended version of the game. (Hint: note that Player 1 now has 4 strategies and write the game up in a 4x2 matrix.) c) Write the game in (b) up in extensive form (a game tree). Identify the subgames of this game.
Consider Bernard \ Mary Left Center Right Top 0,5 1,0 2,2 Bottom 1,0 0,3 2,2 The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5. a Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain.Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC . b Give all mixed strategy Nash equilibria of this game.