A Brief Introduction to
Game Theory
Agenda:
I.
A framework for thinking about
problems
II.
Imperfect competition assumptions
III. The Oligopoly Game
IV. The Prisoner’s Dilemma & Nash
equilibrium
V.
Economic Survivor
VI. The moral of the story…
A Framework for thinking about problems
From Basar & Olsder Dynamic Noncooperative Game Theory (1999) p. 2
One decision maker
Many decision makers
One decision
a series of independent
decisions
Static
Mathematical
programming,
Static
optimization
Static Game
Theory
Multiple related
decisions
Dynamic
Optimal control
theory, Dynamic
optimization
Dynamic or
differential game
theory
Applications of game theory:
Economics, politics, war, infectious disease, engineering,
artificial intelligence, portfolio management, product
development
Models of imperfect competition
Limiting assumption
Monopolistic competition
Each firm pursues optimum
independently; firms respond to profit, but
not specifically to other firms’ actions.
Cournot Ologopoly
Each firm takes the other’s quantity as
given and does not seek to change it.
Stackelberg Ologopoly
The second mover cannot respond to the
first mover’s chosen quantity
Bertrand Ologopoly
Each firm takes the other’s price as given
and does not seek to change it.
Oligopoly Game
Rules of the game:
1. Pick a red or a black card and put it against your chest so no one can see it.
2. I’ll pair you randomly with another player.
3. Show each other your cards and compute your pay-off
Play red card: you get 2 (cut your price)
Play black card: your opponent gets 38(keep your price the same)
4. We’ll play 5 rounds – the first two with random partners and the last three
with the same partner.
5. Highest earners get .5 bonus point (another .5 for the next game…)
(row, column)
Row Player
Black
Red
Column Player
Black
Red
(3,3)
(0,5)
(5,0)
(2,2)
High Gains from Cooperation
Column Player
Black
Red
Black
(8,8)
(0,10)
Row Player
Red
(10,0)
(2,2)
The Prisoner’s Dilemma
Dominant Strategy:
You do better no matter what your
opponent does.
High Gains from Cooperation
Column Player
Black
Red
Black
(8,8)
(0,10)
Row Player
Red
(10,0)
(2,2)
Von Neumann & Morgenstern
Maxmin:
Pick the best of the
worst-case scenarios
Row: 10 or 2 > 8 or 0
Column: 10 or 2 > 8 or 0
Nash Equilibrium:
No player has an incentive to change strategies.
Often one player has a dominant strategy, and the
other chooses a dominant strategy given their
opponent’s dominant strategy.
http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr.
Repeated Games
“Tit for tat”: Cooperate first, but defect if your opponent defects.
“The great enforcer of
morality in commerce is the
continuing relationship”
Frank p. 421
Collusion of bid-ask
spreads on NASDAQ
Richard Kirkland, Battle of Fredericksburg 12/13/1862
http://fredericksburg.com/CivilWar/Battle/kirkland.htm
In essence, the Government found that these firms -- which besides Merrill
Lynch include such Wall Street titans as Goldman, Sachs & Company,
Morgan Stanley & Company and Smith Barney Inc. -- had conspired to
maintain artificially wide margins between the bid price and the ask price
for Nasdaq stocks. Traders who did not follow the market's convention of
only quoting prices in spreads of at least a quarter of a dollar, and tried to
quote in narrower one-eighth increments, were coerced and harassed,
according to Anne K. Bingaman, the Assistant Attorney General in charge
of the department's antitrust division.
http://www.nytimes.com/1996/07/18/business/deal-reached-in-civil-suit-over-collusion-onnasdaq.html
Economics Survivor
Your goal: To get the last card
There will be 21 cards on the table. You can remove 1,2 or 3
cards each turn. The team that removes the last card wins .5
bonus point.
http://en.wikipedia.org/wiki/Nim
Backwards induction – start with where you want to end!
20 the round
before that
16 the round
before that
12 the round
before that
Your opponent
needs to have 8
cards the round
before
If you leave your opponent
with 4 cards, you win!
The moral of the story…
Behavioral
Neoclassical
Game
=
Economic + Economics +
Theory
Theory
Some really cool models of human behavior!
All models are wrong, but some are useful.
“You have to learn the rules of the game. And
then you have to play better than anyone else.”
Albert Einstein