**Homework assignment**

#3 due Oct 29 in class

Answer the following questions for each problem below:

a)

Set up the described game as a normal form

(simultaneous-move) game. Calculate the players’ payoffs and enter them in a

2×2 table (normal form representation of the game).

b)

Find all the Nash Equilibria (NE).

c)

Does Player 1 have a dominant strategy? Explain.

d)

Does Player 2 have a dominant strategy? Explain.

e)

Which payoffs are Pareto efficient (Pareto

optimal)? Is(Are)the NE Pareto efficient? Explain.

You can use Excel file “NE solver

2by2 normal form game” to check your answers to b), c), and d).

**Problem 1.**

Two firms are involved in developing a new technology that

will allow consumers to taste food over the Internet. This has potential, for

example, in restaurant promotion. Given the risks, costs, and a relatively

small expected size of this market, compatibility of the technologies is very

important. Firm DigiTaste (Player 1) is far more advanced in developing its

RemoteTaste technology. WebOdor (Player 2) has been expanding into the Internet

taste arena with its incompatible product, BitterWeb. The two companies agree

that if they both adopt the same technology, they each will gross $200M. If

they adopt different technologies, they each will gross $50M. Retooling one’s

factory to make the competing (nonproprietary) technology would cost WebOdor

$100M and DigiTaste $250M. The production decisions about which technology to

adopt (RemoteTaste or BitterWeb) must be made

simultaneously.

**Problem 2.**

Consider two agents simultaneously deciding whether to

contribute to a public good. (The good is said to be public because, if it is

made available, an agent who free-rides by paying nothing gets just as much

pleasure from its enjoyment as an agent who paid for it.) If at least one agent

contributes to the construction of the public good, both agents will enjoy a

payoff of four from the public good. To

ensure the public good is constructed, player one must pay c1 and player two must

pay c2. Assume that c1=c2=1. If neither contributes, the good is not

constructed and neither player gets enjoyment from the project. If one or both players contribute, then the

good is constructed and each player enjoys a payoff of four minus the

contribution cost if that player has contributed.

**Problem 3.**

Saudi Arabia and Kuwait are engaged in a single-period crude

oil production game? The payoffs are net profits to each from producing

millions of barrels of oil per day. Saudi can produce 4 or 5 million barrels

per day. Kuwait can produce 1 or 2 million barrels per day. If 5 million

barrels per day are produced (in total) then the profit margins are $16 per

barrel. If 6 million barrels per day are produced then the profit margins are

$12 per barrel and they are $8 per barrel if 7million barrels per day are

supplied.

**Problem 4.**

Assume that IBM (Player 1) and Dell (Player 2) have a large

inventory of personal computers that they would like to sell before a new

generation of faster,cheaper machines is introduced. Assume that the question

facing each competitor iswhether or not they should widely advertise a

close-out sale on these discontinueditems, or instead let excess inventory work

itself off over the next few months. If bothaggressively promote their products

with a nationwide advertising campaign, eachwill earn profits of $5 million. If

one advertises while the other does not, the firmthat advertises will earn $20

million, while the one that does not advertise will earn$2 million. If neither

advertises, both will earn $10 million. Assume this is a one-shotgame, and both

firms seek to maximize profits.

**Problem 5.**

Two pizza parlors, 1 and 2, are deciding whether to operate

in an isolated town (enter the market or not). Each will receive profit of $50

if it alone enters. If both enter, each receives $20. Of course, a firm

receives $0 for not entering.

Case 1: Suppose no fee is required to enter the market.

Case 2: Suppose a $30 fee is required to enter the market.