A husband and wife live together in a beautiful little house. Both enjoy having a clean and beautiful house, which is the result of both of their cleaning efforts, but both the husband and the wife dislike putting any actually effort into cleaning. Also, they both value the cleanliness of the house differently.

They each choose a non-negative number, , representing how much effort to devote to cleaning, and each has the utility function

k<1
1. What is the pure strategy Nash equilibrium of this game?
2. How does the distribution of effort in the equilibrium reflect each player's taste for cleanliness? Does this seem fair to you?

In order to find the Nash equilibrium, we must find the best response function of both the husband and the wife. I'll find the one for the husband as a function of k; the function for the wife will be essentially the same (except for the disutility term), for k = 1.

The husband's problem is to choose such that his utility is maximized, given his wife's choice for . Therefore, taking as a given, we find the value of that maximizes by taking the derivative of this function with respect to and equating it to zero. We get:

We now ...

Solution Summary

This job locates the pure strategy Nash equilibrium.

You have been offered the chance to participate in a Treasure Hunt game whose rules are as follows. THere are three coloured boxes: red, green and yellow. The game show host must hide a $100 bill in a box of his choice. You have the option of opening one and only one box/ If the money was hidden in that box, you win it. Otherwis

Below is a payoff matrix for Intel and AMD. In each cell, the first number refers to AMD's profit, while the second is Intel's.
a. Is there a NashEquilibrium(s)? Why or why not?
b. Is this an example of the Prisoner's Dilemma? Why or why not?
Intel
AMD Lower Price Same Price Higher Price
Lower Price

Suppose that a cake is being divided in the following way among two players. Each player writes down a number from zero to one on his piece of paper. Then both players turn over their pieces of paper. If the sum is less than or equal to one, each player gets a share of the cake equal to the number he wrote. If the sum is bigge

Dominant Strategy/NashEquilibrium
Firm 2
Firm 1
Price High Price Low
Price High 400, 350 -80, 800
Price Low 800, -100 200,200
a) Does either firm have a dominant strategy, and if so, what it

Driver 2
Left Right
Driver 1 Left 0,0 -1000 -1000
Right -1000, -1000 0,0
-Does either player have a dominant strategy?
-Is there a Nashequilibrium in this game? Explain
-Why is this game called a coope

Suppose two firms, Firm Y, Inc., and Firm X, Inc., are locked in a bitter pricing struggle in the bottled water industry. In strategy A, pricing payoff matrix, Firm Y can choose a given row of outcomes by offering A price ("up") or B price ("down"). Firm X can choose a given column of outcomes by choosing to offer A price ("left

Game:
C1 C2 C3
R1 3,2 2,1 1,a
R2 2,2 b,4 0,2
R3 c,d 3,2 e,4
a) Give a condition on b such that R2 is strictly dominated by R1.
b) Given that a) holds, find a condition on d such that C1 strictly dominates C2.
c) Given that a) and b) hold, find conditions on a and c such that (R1, C1) is a Nashequilibrium.
d) Give

Suppose two competitors, Coa, Inc., and Han, Inc., are locked in a bitter pricing struggle in the aluminum industry. In the limit pricing payoff matrix, Coa can choose a given row of outcomes by offering a limit price ("up") or monopoly price ("down"). Han can choose a given column of outcomes by choosing to offer a limit price

Try to Understand the Different Types of Strategy
4 - 5 Questions will be on mid-term. Use the below information for a study guide!! If you understand this type of game of strategy, you will do fine!!
Also study the Prisoner's Dilemma (Already Understand)
Note to Self: Continue to work on additional study guide materi