There are 3 workers W1,W2,W3. Neither of these workers can be employed alone so that their value for remaining single is 0. The pair W1 and W2 if employed jointly can earn 100. Likewise the pair W1 and W3. Say the pair W2 and W3 if employed jointly can earn z. The three workers cannot be employed together. What is the maximum value for z such that there is a stable matching in this game ?

There are 3 workers W1,W2,W3. Neither of these workers can be employed alone so that their value for remaining single is 0. The pair W1 and W2 if employed jointly can earn 100. Likewise the pair W1 and W3. Say the pair W2 and W3 if employed jointly can earn z. The three workers cannot be employed together. What is the maximum value for z such that there is a stable matching in this game ?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

See similar textbooks

Similar questions

In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
David wants to auction a painting, and there are two potential buyers. The value for eachbuyer is either 0 or 10, each value equally likely. Suppose he offers to sell the object for $6, and the two buyers simultaneously accept or reject. If exactly one buyer accepts, the object sold to that person for $6. If both accept, the object is allocated randomly to the buyers, also for $6. If neither accepts, the object is allocated randomly to the bidders for $0. (a) Identify the type space and strategy space for each buyer. (b) Show that there is an equilibrium in which buyers with value 10 always accept. (c) Show that there is an equilibrium in which buyers with value 10 always reject.
Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? 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.
Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 4 pure strategies and Bob has 3 pure strategies. How many pure strategies does Alice have in the repeated game?
Three players (player 1, player 2 and player 3) each chooses a positive integer QE {1, 2, 3, . 100}. If all three players choose the same integer Q, each player gets $100/3. If all three players choose different integers, the player with the largest integer gets $100, and the two other players get $0. If two players choose the same integer Q, and the third player chooses a different integer Q', then the player playing Q' gets $0, and the two players who played Q get $50 each. Find 2 Nash equilibriums in this game. ....
$11. Anne and Bruce would like to rent a movie, but they can't decide what kind of movie to get: Anne wants to rent a comedy, and Bruce wants to watch a drama. They decide to choose randomly by playing "Evens or Odds." On the count of three, each of them shows one or two fingers. If the sum is even, Anne wins and they rent the comedy; if the sum is odd, Bruce wins and they rent the drama. Each of them earns a payoff of 1 for winning and 0 for losing "Evens or Odds." (a) Draw the game table for "Evens or Odds." (b) Demonstrate that this game has no Nash equilibrium in pure strategies.
Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…
Tom and Jerry are each given one of two cards. One card is blank, while the other has a circle on it. A player can draw a circle on the blank card or erase the circle on one that has already been drawn. Tom and Jerry make their decision separately and hand in the card at the same time.Nobody wins anything unless the two cards are handed in with one and only one circle on them. The player who hands in the card with the circle receives $20, while the one who hands in the blank card receives $10. Answer the following questions. (1) Represent the game in strategic form.(2) Find the Nash equilibria of the game (in pure strategies).
There is a beach with nine regions in it and two pop sellers must choose in which region to situate. Customers in each region walk to the closest seller to buy a pop. Each pop is sold for $1 each. Suppose that the customers are not distributed evenly across the regions. Regions 2 through 9 each have 10 customers but region 1 has x customers. For what values of x does the strategy of locating in region 2 dominate locating in region 1? In particular, what is the maximum value of x for this to be true? Please show all your calculations in your written solution.
With what probability does player 1 play Down in the mixed strategy Nash equilibrium? (Input your answer as a decimal to the nearest hundredth, for example: 0.14, 0.56, or 0.87). PLAYER 1 Up Down PLAYER 2 Left 97,95 47, 33 Right 8,43 68,91
The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.