The board of a football club consists of three extremely wealthy owners and five fans of the club. To decide on a proposal, the board uses a voting game in which all three wealthy owners and at least two fans must vote in favour in order for the proposal to be accepted. (a) Show that the voting game use by the board for deciding whether to approve a motion can be weighted. (b) For the voting game used by the board, find the Shapley-Shubik index of each fan. Hence, or otherwise, find the Shapley-Shubik index of each extremely wealthy owner.

The board of a football club consists of three extremely wealthy owners and five fans of the club. To decide on a proposal, the board uses a voting game in which all three wealthy owners and at least two fans must vote in favour in order for the proposal to be accepted. (a) Show that the voting game use by the board for deciding whether to approve a motion can be weighted. (b) For the voting game used by the board, find the Shapley-Shubik index of each fan. Hence, or otherwise, find the Shapley-Shubik index of each extremely wealthy owner.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.16P

See similar textbooks

Similar questions

The board of a football club consists of three extremely wealthy owners and five fans of the club. To decide on a proposal, the board uses a voting game in which all three wealthy owners and at least two fans must vote in favour in order for the proposal to be accepted. (a) Show that the voting game use by the board for deciding whether to approve a motion can be weighted. (b) For the voting game used by the board, find the Shapley-Shubik index of each fan. Hence, or otherwise, find the Shapley-Shubik index of each extremely wealthy owner. (c) Suppose that the board changes the voting game used to decided whether to ap- prove a proposal so that, in order to be approved, at least two extremely wealthy owners and at least three fans must vote in favour of the proposal. Can this voting game be weighted? Brieflv justifv vour answer.
A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.
Economics The trust game is a two player game with three stages, often used in economics exper- iments to measure trust and trustworthiness. Player 1 starts off with 10 Dollars. She can send an amouh 0 SI S 10 to player 2. The experimenter triples the sent amount such that player 2 receives 3r. Player 2 can then send an amount 0
Please do the both questions
0 E F 3 2 FIGURE 2 23 D G 2 H 0 1 (2) Two friends, Albert (A) and Berta (B), have to decide on going to one of three bars, Xenia's (X), Yara's (Y), or Zana's (Z). They decide to select a bar by alternatively vetoing bars until one remains. First Albert vetoes a bar. If at least two bars remain, then Berta vetoes another bar. That process continues until a single bar remains unvetoed. Suppose Albert prefers Xenia's to Yara's to Zana's and Berta prefers Zana's to Yara's to Xenia's. Assume that, for each of the two, going to their most preferred bar gives a utility of 2, going to their next preferred bar gives a utility of 1, and going to their least preferred bar gives a utility of 0. Model this as an extensive form game and find its Nash equilibria. Which of the Nash equilibria are subgame perfect?
Please no written by hand and no emage Two classmates A and B are assigned a group project. Each student can choose to Shirk or Work. If one or more students chooses Work, the project is completed and provides each with credit valued at 4 payoff units each. The cost of completing the project is that 6 total units of effort (measured in payoff units) is divided equally among all players who choose to Work and this is subtracted from their payoff. If both Shirk, they do not have to expend any effort but the project is not completed, giving each a payoff of 0. The instructor can only tell whether the project is completed and cannot determine which students contributed to the project. A. Write down (draw) the normal form game, with payoff in the format of (player A payoff, player B payoff). Note that we assume students choose to Shirk or Work simultaneously. B. Does either player have a dominant strategy? C. Find the Nash equilibrium or equilibria. D. Explain ‘Prisoners’ dilemma’ using the…
Two politicians from the same party decide whether to support or oppose the gov- ernment's environmental policy. Politician A prefers that they both support, but Politician B prefers that they both oppose. Both politicians agree that the party should have a coherent position and the worst outcome is that one supports and the other opposes the policy. (a) Formulate this situation as a strategic game - specify the players, actions, and payoffs (you can set-up a table of the actions and payoffs). (b) What are the Nash equilibria of this game? Explain your answer.
This is 3 sub part of 1 question so answer completely. you will get up vote for correct and complete answer and vice versa
Player Rhas a $2, a $5, and a $10 bill. Player Chas a $1, a $5, and a $10 bill. Each player selects and shows (simultaneously) one of his or her three bills. If the total value of the two bills shown is even, Rwins Cs bill; if the value is odd, Cwins Rs bill. (Which player would you rather be?) (A) Set up the payoff matrix for the game. (B) Solve the game using the simplex method discussed in this section. (Remove any recessive rows and columns, if present, before you start the simplex method.)
Find the winner of this election under the Borda Count method. Number of voters DO OC B OA D 5 4 A B C B D D A 1st choice 2nd choice C 3rd choice 4th choice 6 C A D B 5 D A C B 11 D B C A
-3 1 Consider the game defined by the matrix: P = 4 -3 IO 10 61 ooloulote the matrix RP to determine
3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760