Economics Homework Help

Q1)

For each game, identify

a) all strategy proles which survive iterated elimination of strictly dominated strategies,

b) all strategy proles which survive iterated elimination of weakly dominated strategies,

c) all Nash equilibria (pure strategies).

In each game, payos are in alphabetical order. That is, in a given cell, the rst number is Ann’s

utility and the second number is Bob’s utility. You can gain up to 10 points per each game.

Q2)

An airline loses two suitcases belonging to two dierent travelers, Ann and Bob. Both suitcases

happen to be identical and contain identical items (antiques). An airline manager tasked to settle

the claims of both travelers explains that the airline is liable for a maximum of 500 per suitcase.

(The manager is unable to nd out directly the price of the items.) In order to determine an

honest appraised value of the antiques the manager separates both travelers so they can’t confer,

and asks them to write down the amount of their value. For simplicity, assume that the value can

be one of the following numbers: 100 SAR, 200 SAR, 300 SAR, 400 SAR, or 500 SAR.

The manager explains that if both write down the same number, then he will treat that number

as the true SAR value of both suitcases and reimburse both travelers that amount. However, if

one writes down a smaller number than the other, this smaller number will be taken as the true

SAR value, and both travelers will receive that amount along with a bonus/malus: 10 SAR extra

will be paid to the traveler who wrote down the lower value and a 10 SAR deduction will be taken

from the person who wrote down the higher amount.

Q3)

In this exercise, your job is to invent and solve a two-player game. Think about some interactive

problem from your professional or personal life. Then, express that problem in the language of

game theory (matrix), and solve it (Nash equilibria).

It is important that what you propose is original. That is, what you analyze must be your own

invention. Your task is to put on the hat of applied game theorist: you analyze some problem

using the game-theoretic tools. You can think of your job as consisting of three steps.

Q4)

Two students { Ann and Bob { simultaneously download music over the campus computer network.

Let si 0 represent the total size of student i’s music download, where i stands for either Ann

or Bob. Each student i decide on his/her own. In other words, there is no communication or any

form of cooperation. Ann and Bob play a static game.

The more data is being downloaded, the slower the network functions. The total time it takes

for student i’s songs to download depends on both the size of his/her download, and on the total

amount of data that the network has to deliver.

Each student benets from the size of his/her music download but is hurt by the time spent

waiting for the music download to nish. In particular, we assume that the total amount of time

it takes for player i to download his/her music is given by ci(sA; sB) = si(sA + sB); this is a cost

function of player i. At the same time, player i enjoys benet si. Hence, the utility function of

player i is described by the following equation.

ui(sA; sB) = si si(sA + sB)