Download oligopoly, strategy and game theory

OLIGOPOLY, STRATEGY AND GAME THEORY:
SOME TEACHING NOTES
GREGORY H. WASSALL
NORTHEASTERN UNIVERSITY
I. Introducing to the Topic
A. Useful knowledge
1. be sure that the students understand the basic ideas of an oligopoly
industry
2. it is often useful to cite examples of such industries:
a. (identical product) steel, aluminum, copper, oil refining
b. (differentiated product) automobiles, cigarettes
3. focus on the concept that any one firm=s actions are likely to trigger a
reaction by its competitors; before the first firm acts, it must
consider these reactions= i.e., it must behave strategically
4. as a result, unlike the other industry structures we study, there is no
one model or diagram that describes the situations that oligopolistic
firms find themselves in, or the choices they have to make
5. game theory provides a relatively simple approach to analyzing
situations where strategy matters
II. Types of Games and Game Definitions
A. What is a game?
1. features of games
a. they have rules which govern allowed actions, order of actions,
and how the outcome of the game is related to the actions
taken
b. they involve two or more players, each trying to do the best for
herself
c. each player's outcome depends of the actions of the other
players, and each player knows this
2. games of strategy: a player's payoff is affected by his actions and
those of other players; examples are chess and poker, but they
also include things like pricing, entry and other economic
phenomena
3. non-cooperative game: players are unable to make legally binding
contracts with one another, due to the game's rules; the unit of
analysis is the individual player
a. examples: chess, poker, firms in oligopolistic competition
4. co-operative game: players can talk to each other and enter into
legally binding contracts; the unit of analysis often is a group, or
coalition
a. examples: bargaining, such as labor-management, formation
of political coalitions, the core of an economy
b. most principles of economics textbooks do not cover cooperative games; however, they are often used to model
collusion in oligopoly, as well as coalitions in political
strategy and public goods
5. other academic applications of game theory include political science,
biology, and war strategy
B. A way to describe non-cooperative games: strategic or normal form
1. this is the usual way that a game situation is described in a principles
of economics textbook
1. the normal form consists of
a. a list of participants, or players
b. for each player, a list of strategies
c. for each array of strategies, one for each player, a list of payoffs
that the players receive
d. simultaneous decisions
2. since the strategy dictates what a player does, he could dictate it for a
stand-in; thus it would have to be complete
III. Introducing Some Game-Playing
A. Consider this game: the original prisoner=s dilemma
PRISONER B
PRISONER A
Don't Confess
Confess
Don't Confess
-1,-1
-10,0
Confess
0,-10
-5,-5
This is the classic prisoner=s dilemma game, shown in a payoff matrix. The
authorities capture two persons who they strongly believe have committed a crime.
However, they only have enough evidence to convict them of a minor offense (1 year in
jail) if no one confesses. So the prisoners are put in separate rooms, where they
cannot communicate (a la NYPD Blue). A prisoner who confesses gets immunity goes
free; the other gets a 10 year jail term. If both confess, they each get 5 year terms,
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because of their cooperation
1. ask the class what they would do in this situation; work the discussion
toward a Abest@ strategy
2. ask if that strategy would be different if the prisoners were able to
communicate with each other
B. Now consider this pricing game
COMPANY B
COMPANY A
High Price
Low Price
High Price
5,5
-2,8
Low Price
8,-2
0,0
These companies are the only sellers of the same product. If they compete for
customers, they both set aggressively low prices, and each winds up with $0 profit.
However, if they cooperate (collude), they will act like a joint monopoly and set a profitmaximizing price, earning each a profit of $5 million. However, if one cheats on the
agreement by cutting price, its profit rises to $8 million, and the other=s falls to $-2
million. Again,
1. ask the class what they would do in this situation; work the discussion
toward a Abest@ strategy
2. ask what they might do to try to maintain cooperation, if they are in
Acheating mode; consider OPEC as an example. Does playing the
game repeatedly (unlike the prisoner=s dilemma above, which is
played once) make a difference?
C. One last game: an advertising game
COMPANY Y
COMPANY X
Don=t Advertise
Advertise
Don=t Advertise
10,10
2,15
Advertise
15,2
7,7
This describes the payoff matrix for two sellers producing similar products in the same
market (e.g., beer or cigarettes). Their profits are net of advertising. Will these firms
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spend money on advertising? Is it in their best interests to do so?
IV. Equilibria in Games: Where Do the Above Examples Lead Us?
A. ASolving@ these games
1. are there techniques that lead one to the optimal strategy in each
case? See below
B. Dominant Strategy Equilibrium
1. strict dominance: in a normal-form game, a strategy 1 is strictly
dominated by strategy 2 if every payoff from playing strategy 1 is
strictly dominated by the corresponding payoff from playing
strategy 2
2. weak dominance: every payoff from strategy 2 is at least as good as
the corresponding payoff from strategy 1
3. dominance allows to eliminate from consideration strategies that are
dominated
4. consider the first prisoner=s dilemma game above: each prisoner=s
dominant strategy is to confess, although the best outcome for both
(least aggregate jail time) is not to confess; this requires
cooperation
5. in the pricing and advertising games, a prisoner=s dilemma outcome
occurs again; this outcome is reinforced by the illegality of collusion
in U.S. anti-trust law
C. Nash equilibrium
1. definition: a set of strategies, one for each player, such that no player
has an incentive (in terms of improving his own payoff) to deviate
from his strategy, i.e., each player can do no better given what the
opposing player(s) does
2. an example of Nash equilibrium lies above, in the prisoner's dilemma
games
3. how to determine a Nash equilibrium: check a strategy option for
player A; is player B's response the best to player A's strategy?; is
player A's strategy the best response to player B's?
4. note that Nash equilibrium is the first game is Confess, Confess (what
about the others?)
5. what if the prisoners could communicate?
VI. Some other classic games, and oligopoly equivalents
A. Battle of the sexes (please excuse the stereotyping)
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HUSBAND
WIFE
Football
Ballet
Football
4,5
0,0
Ballet
1,1
5,4
Wife prefers ballet, Husband prefers boxing, but both prefer each other's company.
What do they choose?
1. here there is no dominant strategy, but F,F and B,B are Nash equilibria
2. oligopoly applications: two manufacturers of complementary products
debating standards, e.g. VHS vs. Betamax, or two incompatible wifi network products; also two or more states debating adopting the
same income tax rules
B. Chicken
DRIVER 2
DRIVER 1
Hang tough
Chicken
Hang tough
0,0
3,1
Chicken
1,3
2,2
Two persons drive automobiles toward each other at top speed. Just before they
collide, each chooses to maintain direction (hang tough) or swerve (chicken). If both
swerve, no one is embarrassed and they are satisfied. If one swerves and the other
does not, the Aswerver@ is embarrassed in front of his buddies and girl friend, and the
other is praised as a tough guy. If neither swerves, each is badly injured and they lose
their girl friends.
1. again, there is no dominant strategy, but HT, C and C,HT are Nash
equilibria
C. An oligopoly version of this game lies below: R&D expenditures
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FIRM 2
FIRM 1
No R&D
R&D
No R&D
0,0
1,10
R&D
10,1
5,5
Here two competing firms engage in R&D that leads to an improved product, but that
the technology for the improved product cannot be kept secret or patented. Both firms
benefit from the R&D of either firm. The question is: does each firm chicken and spend
on R&D, or hang tough and not spend on R&D (but free ride on the other=s R&D)?
1. same as above, there is no dominant strategy, but Nash equilibria exist
at R&D, No R&D, and No R&D, R&D
.
VII. A Second Way to Describe Non-Cooperative Games: Repeated and Sequential
Games
A. Repeated games
1. if firms play a game repeatedly, it becomes possible for one firm to
penalize the other for previous bad behavior, or to encourage
cooperation
2. options in the pricing game
a. cooperative behavior
b. tit-for-tat: one firm cooperates in the current period if the other
cooperated in the previous period, but cheats in the current
period if the other cheated in the previous period
c. trigger strategy: one firm cooperates if the other cooperates,
but plays the Nash equilibrium strategy every period if the
other cheats
B. Sequential games
1. a shortcoming of the normal form is that it cannot describe sequential
decision-making
2. extensive form game; in this form, attention is given to the timing of
actions that players may take and the information they have when
they must take these actions; it consists of
a. nodes, a position in the game
b. vectors of numbers, representing payoffs
c. directional lines, which point from some nodes to the others, and
to the vectors
d. labels for the nodes and lines
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3. a generic extensive form is mapped at the end of this handout
4. the extensive form better delineates sequential moves in games
VIII. Entry With Sequential Decisions
A. Economics of the example
1. an incumbent monopoly faces a potential entrant
2. first stage: incumbent decides whether to take action to prevent entry
3. second stage: potential entrant decides whether to enter
4. if entry occurs, they act like duopolists
B. Blocking entry
1. if entry is not blocked by market conditions, it may become necessary
to take action to block entry
2. incumbent incurs a cost to block entry (lowering price, e.g.)
3. entry is successfully blocked if the duopoly profit from entry is negative
4. entry is blocked only if the new firm must incur a fixed cost to enter
C. Commitment and entry prevention
1. in order to successfully block entry, the incumbent firm must have a
credible threat
2. not all firms can make credible threats
3. non-credible threat: producing large output to deter entry would cause
incumbent to lose money
4. many examples of this behavior in the airline industry with route entry
5. example: incumbent=s strategy depends on fixed costs of incumbent
a. decision to enter is predicated on fixed costs of entry
b. incumbent firm=s decision of how much to produce is predicated
on entrant=s profits
Note: Most microeconomics texts have introduced some amount of game theory in the
oligopoly chapter. A good non-technical reference on game theory and strategy and
game theory is general is A. Dixit and B. Nalebuff, Thinking Strategically (New York:
Norton, 1993).
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Representing a dynamic game in extensive form.