Dominant Strategy:


Introduction:

A strategy that is always better than any of the other strategies that is available to a player,
regardless of what strategy any other player decides to choose. The classic example is the
prisoner dilemma, were two prisoners have to decide to either keep quiet or to rat out a fellow
partner in crime in order to better their position. Other examples can be found in TV games
shows and even in poker. In addition, all dominant strategy equilibriums are a Nash Equilibrium.

Some real world examples of Dominant Strategy are:
a)
State Governments competing against other states in order to attract businesses to locate
in their state. Some recent examples in the news were the Honda and Toyota automobile plants.
Several Mid-Western states were offering various incentive packages to lure these companies to
locate in their state.

b) Unions bargining for better labor contracts with a company for their members.

c) Cycle racing where the two lead cyclists must decide when to lead and when to follow, if they
do not work together the rest of the pack will catch up to them, if one decides to try to lead the
entire time, he will likely end up losing since the follower will have more energy at the end due to
being sheltered from the wind by the leader. Both will be forced to work together in order to keep
their dominant position.


External Links and references:

1) Managerial Economics and Business Strategy (5th Edition) – Michael R. Baye
2) Game Theory .net
3) Journal of Economic Education – Spring 1999 Pages 133:140 – Gregory A. Trandel
4) Dominance (game theory)
5) Nash Equilibrium:

Example Multiple Choice Questions:

QUESTION 1:
Dominant Strategy is:
a) strategies that benefit a player
b) strategies that benefit the other players
c) strategy with the best results regardless of what other players do
d) strategy with the best results only if the other players also choose it

Answer is c. The dominant strategy must provide the best benefit available without any regard
of that the other player does.

QUESTION 2:
There are two ice cream makers in the town of Smallville. One is Bob and Jones (BJ) and one
is King of Dairy (KD). They are the only two ice cream makers in this market. Each of them is
preparing for the summer ice cream season. For that preparation, they have to choose whether to
advertise or to not advertise. The payoffs are below:

ADVERTISE DECISION BJ, ADVERTISE DECISION KD, PAYOFF BJ, PAYOFF KD
Advertise, Advertise, 200, 100
Advertise, Don't Advertise, 250, 50
Don't Advertise, Advertise, 50, 250
Don't Advertise, Don't Advertise, 100, 50

Now, do either, or both of them, have a dominant strategy?

(a.) Neither of them have a dominant strategy.
(b.) BJ has a dominant strategy, but KD does not.
(c.) KD has a dominant strategy, but BJ does not.
(d.) They both have a dominant strategy.

Answer is d. They both have a dominant strategy. No matter what KD does, BJ is always better off
advertising. No matter what BJ does, KD is better off advertising.

QUESTION 3:
There is only one musical band in Smallville, called the Funky Bunch (FB). A musician is
considering entering the market. His name is Marky Mark (MM). The funky bunch does not like
Marky Mark very much, so they are considering whether to launch attack advertisements on
television talking about how horrible Marky Mark would be for the music industry.

The payoffs are below:



FB
FB


ATTACK
DO NOT ATTACK
MM
ENTER
100, 400
200, 300
MM
DO NOT ENTER
0, 400
0, 500

Question 3A: Does FB have a dominant strategy? If so, what is it?
Question 3B: Does MM have a dominant strategy? If so, what is it?
Question 3C: What is the payoff for both MM and FB in this example?
Question 3D (BONUS): Does this represent a Nash equilibruim?

Answers:
Question 3A:
FB does not have a dominant strategy. If MM enters, then FB is better off attacking.
If MM does not enter, then FB is better off not attacking.
Question 3B: MM does indeed have a dominant strategy. No matter what FB does, MM is better
off entering the music industry.
Question 3C: Since MM has a dominant strategy, he will enter. Therefore, FB will choose to attack him.
So the payoff for MM and FB are, respectively, 100, 400.
Queston 3D (BONUS): Yes, this is a Nash equilibrium! Good job! Neither player can improve his or her
payoff by unilaterally changing his or her strategy, given the other player's strategy.