Compute set of rationalizable effort levels for each player

Assignment Help Game Theory
Reference no: EM13964813

Three game theorists work on a team project. Assume they work independently, and it is not possible for them to monitor each other. No one likes working, and the cost of efforts is measured in dollars. Each player can work up to 5 hours, and the cost per working hour is $6. The quality and hence the profit of the project is determined by the joint efforts (total number of working hours) of the three players. For each additional hour that the team invests in the project, up to 10 hours, the total profit will increase by $15. After 10 hours, efforts will not increase profits. Assume players divide the profit equally among them. Hence, each player's payoff is his share of the profit minus his cost. There is common knowledge of rationality.

(a) What is the strategy space (the set of strategies) for each player?

(b) What is the payoff for each player as a function of the strategy profiles?

(c) Compute the set of rationalizable effort levels for each player.

(d) Suppose one player is kicked out of the team, and the remaining two players still share the profit equally. Compute the set of rationalizable effort levels.

Reference no: EM13964813

Questions Cloud

Determine the temperature of the surface of the steam kettle : Determine the temperature of the surface of the steam kettle that is in contact with the stove.
Find an elementary matrix : Is it possible to find an elementary matrix E such that EB = C? Justify your answer in a proof. Write the matrix 3 -2 as a product of elementary matrices.
What is highest fundamental frequency that this string have : What is the length of the longest and thinnest string that can be placed under a tension of 890 N without breaking?
Compute the product by inspection : 1. Compute the product by inspection. 2. Use the given equation to determine by inspection whether the matrices on the left commute.
Compute set of rationalizable effort levels for each player : What is the strategy space (the set of strategies) for each player? What is the payoff for each player as a function of the strategy profiles? Compute the set of rationalizable effort levels for each player.
Differences between pasteurization,commercial sterilization : The discussion should be based on the processing method involved and preservation principles behind each method. In addition, what will be the shelf-life expectancy for food products treated by each one of these methods?
What change in magnetizing force required to decrease flux : What change in magnetizing force is required to decrease the flux density of magnetic material from a saturation in the positive direction to zero.
Unbounded self-adjoint operator : Let H be the unbounded self-adjoint operator defined by -d^2/dx^2 (the negative of the second derivative with respect to x) on: D(H) ={f element of L^2 | Integral( |s^2 F f(s)|^2 )ds element of L^2}
Problem regarding the basic matrix laws : Let A and B be arbitrary n x n matrices whose entries are real numbers. Use basic matrix laws only to expand (A + B)². Explain all steps. Hint: Use the distributive laws.

Reviews

Write a Review

Game Theory Questions & Answers

  Use the best-response approach to find all nash equilibria

Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.

  A supplier and a buyer, who are both risk neutral

A supplier and a buyer, who are both risk neutral, play the following game,  The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.

  Pertaining to the matrix game theory problem

Pertaining to the matrix need simple and short answers, Find  (a) the strategies of the firm (b) where will the firm end up in the matrix equilibrium (c) whether the firm face the prisoner’s dilemma.

  Nash equilibria

Consider the two-period repeated game in which this stage game is played twice and the repeated-game payo s are simply the sum of the payo s in each of the two periods.

  Find the nash equilibrium

Two players, Ben and Diana, can choose strategy X or Y. If both Ben and Diana choose strategy X, every earns a payoff of $1000.

  Construct the payoff matrix for the game

The market for olive oil in new York City is controlled by 2-families, Sopranos and Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter New York City olive oil market.

  Question about nash equilibrium

Following is a payoff matrix for Intel and AMD. In each cell, 1st number refers to AMD's profit, while second is Intel's.

  Finding the nash equilibrium

Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.

  Nash equilibria to determine the best strategy

Little Kona is a small coffee corporation that is planning entering a market dominated through Big Brew. Each corporation's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price.

  Creating a payoff table

Suppose you and your classmate are assigned a project on which you will earn one combined grade. You each wish to receive a good grade, but you also want to avoid hard work.

  Determine the nash equilibrium for trade policy

Consider trade relations in the United State and Mexico. Suppose that leaders of two countries believe the payoffs to alternative trade policies are as follows:

  Find the nash equilibrium outcomes

Use the given payoff matrix for a simultaneous move one shot game to answer the accompanying questions.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd