3. Consider a variant of the Rubinstein bargaining game with two players where player 1's discount factors is d1 and player 2's discount factor is 82: a) In cach round player 1 makes a proposal and player 2 says “yes" (game over) or “no" (continues to the next round). Find SPE-play and the SPE. b) In round 1 player 1 makes a proposal and players 2 says "yes" (game over) or says "no" (continues to the next round). From round 2 onwards, in each round, player 2 makes a proposal and player 1 is the responder ("yes" = game ends, "no" = continues to the next round). Determine SPE-play and the SPE. %3D %3D

3. Consider a variant of the Rubinstein bargaining game with two players where player 1's discount factors is d1 and player 2's discount factor is 82: a) In cach round player 1 makes a proposal and player 2 says “yes" (game over) or “no" (continues to the next round). Find SPE-play and the SPE. b) In round 1 player 1 makes a proposal and players 2 says "yes" (game over) or says "no" (continues to the next round). From round 2 onwards, in each round, player 2 makes a proposal and player 1 is the responder ("yes" = game ends, "no" = continues to the next round). Determine SPE-play and the SPE. %3D %3D

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 10E

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4 Consider an extensive game where player 1 starts with choosing of two actions, A or B. Player 2 observes player 1’s move and makes her move; if the move by player 1 is A, then player 2 can take three actions, X, Y or Z, if the move by player 1 is B, then player 2 can take of of two actions, U or V. Write down all teminal histories, proper subhistories, the player function and strategies of players in this game.
(a) Find all the Nash Equilibria, if there is any. (no explanation needed for this part (b) Does player 1 (choosing rows) have any dominant action? If yes, which action(s)? Any dominated action(s)? If yes, which ones? Answer the same questions for player 2, too. (c) If player 1 moves first (and player 2 moves next), what would be the sequentially rational equilibrium (draw the game tree and use backward induction)?What if player 2 moves first (and then player 1 moves next)? (d) Looking at your findings in (c), would player 1 want to move first or second or is she indifferent (the order doesn’t matter)?
answer the ff: Suppose that each company cancharge either a high price for tickets or a low price. Ifone company charges $300, it earns low profit if theother company also charges $300 and high profit ifthe other company charges $600. On the other hand,if the company charges $600, it earns very low profit ifthe other company charges $300 and medium profitif the other company also charges $600.a. Draw the decision box for this game.b. What is the Nash equilibrium in this game?Explain.c. Is there an outcome that would be better than theNash equilibrium for both airlines? How could itbe achieved? Who would lose if it were achieved?
3. Three politicians are voting on whether to allow themselves a salary increase of $ 3,500 per year. If they vote in favour of a raise, then they lose some public support, costing them each $ 1,500 per year. The salary increase passes if two or more politicians vote in favour of it. What is this game’s Nash equilibrium (or equilibria)? Explain. There is no need to draw a payoff matrix. (20%
Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
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.
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?
Consider the location game we covered in Lecture 3. Now assume there arethree players (vendors). As we assumed in the lecture, consumers in each area choosethe closest vendor and if there are multiple closest vendors then these vendors receiveequal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here aresome examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1?(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?(c) Can you find a Nash equilibrium in pure strategies?
Consider the strategic voting game discussed at the endof this chapter, where we saw that the strategy profile (Bustamante, Schwarzenegger,Schwarzenegger) is a Nash equilibrium of the game. Show that (Bustamante, Schwarzeneg-ger, Schwarzenegger) is, in fact , the only rationalizable strategy profile. Do this by firstconsidering the dominated strategies of player L. (Basically, the question is asking youto find the outcome of the iterative elimination of strictly dominated strategies)
1) Suppose that Player A can take two actions, either Up or Down. Player A is thinking to choose Up 50 percent of the time, and Down 50 percent of the time. This type of strategy is called a ____ ? 2) Consider a payoff matrix of a game shown below. In each cell, the number on the left is a payoff for Player A and the number on the right is a payoff for Player B. In order for (Down, Right) to be a unique pure strategy Nash equilibrium, a must be (greater, or smaller) than 3 and b must be (greater, or smaller) than 3. refer to image
1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?