Ch.1. Introduction:
Game and Game Theory
LIST
1.1 What is a game theory?
1) game theory and game
2) what is a game?
3) Game theory
1.2 Classifications of games and the outline of this
lecture
1) cooperative vs. non-cooperative game
2) perfect vs. imperfect game
3) complete vs. incomplete game
1.3 Evaluation of Game Theory
1) Rubinstein
2) Nash’s Nash Equilibrium
3) Nobel Prize in economics, 1994
4) Applications
1.1 What Is a Game Theory?
1) game and game theory
Game theory emanates from studies of amusement games
such as chess or poker.[The first theorem in game theory is
Zermelo’s theorem on Chess(1913)].
However, game theory is no longer concerned with
amusement games.
Zermelo’s Theorem
asserts that in chess either white can force a win, or black can
force a win, or both sides can force at least a draw.
2) What is a game?
a) A game in everyday life :
a universal form of recreation generally including any activity engaged in
for diversion or amusement and often establishing a situation that
involves a contest or rivalry (http://www.britannica.com/)
Ex) board games, card games, video games, field games, etc.
b) a game in game theory :
any rule-governed situation with well-defined outcome, characterized by
strategic interdependence.(Gardner, p.4)
c) comparison.
Games in game theory
(1) exclude non-interactive games:
athletic sport(100m, ..., marathon, race, etc), golf,
-- no interaction except for psychological effects
(2) include game-like socio-economic situations .(main object
of study)
oligopoly, trading process(auctions, bargaining),
employment and promotion, valuation of firm values,
international trade policy, macroeconomic policy
decision,voting, etc
-> economics, business, sociology, politics, biology, …
3) game theory
It studies multiperson, or interdependent, decision problems.
It can be defined as the study of mathematical models of
conflict and cooperation between intelligent rational
decision-makers.
--> more descriptively accurate names: "Conflict analysis" or
"interactive decision theory" (R.B.Myerson, Game Theory:
analysis of conflict, Harvard Univ. Press, 1991, p.1)
1.2 Classifications of games and the
outline of this lecture
1) cooperative vs. non-cooperative game
A game is non-cooperative if players can not make
binding commitments(or agreements), and
cooperative otherwise, irrespective of the possibility of
communications.
Unit of analysis is an individual player in non-
cooperative games, and a group(coalition) in cooperative
games.
We do not deal with cooperative games.
2) perfect information vs. imperfect information game
Perfect information = at each move in the game, the player with the
move knows the full history of the play of the game thus far.(p.121)
ex) chess, football, English auction
Sequential and open moves -> [dynamic games] = games with more
than 2 stages
Imperfect information game = a player does not know what others did.
ex) sealed bid auction, game of rock, paper, scissors.
Simultaneous and secret moves -> [static games] = games with a
single stage
3) complete information vs. incomplete information game
Incomplete information = at least one player is uncertain about
another player’s payoff function. [Asymmetric or private
information]
Ex) Firm’s MC and workers’ ability may be private information.
4) Contents of our textbook
Complete Incomplete
Imperfect Chapter 1 Chapter 3
(static) [Nash Equilibrium] [Bayesian NE]
Perfect Chapter 2 Chapter 4
(dynamic) [Subgame Perfect NE] [Perfect Bayesian NE]
1.3 Evaluation of Game Theory
1) Rubinstein
("Introduction" in Game theory in Economics, eds by A.
Rubinstein, 1990, p.xi)
1950’s-- era of general equilibrium
1960’s-- era of growth
1970’s—era of economics of information
1980’s – era of game theory
2) Nash’s Nash Equilibrium
( R.B. Myerson, "Nash Equilibrium and the History of Economic Theory,"
Journal of Economic Literature, 37(3), September 1997, 1067-1082)
Nash's theory of noncooperative games should now be recognized as one
of the outstanding intellectual advances of the twentieth century,
comparable to the discovery of the DNA double helix in the biological
sciences.(p.1067)
Why? – It provides a general analytical framework (methodology) for
extending rational-choice analysis to non-market applications. (p.1069)
So, economics could change
from (marginalist era) social science concerned with the production
and allocation of material goods
to (today) the analysis of incentives in all social institutions.
※ Nash’s papers
―Equilibrium Points in n-Person Games,‖
Procedings of National Academy Sciences, 1950,
48-49 (Two pages)
―Noncooperative games,‖ The Annals of
Mathematics, 1951, 289- 295(Ph.D Thesis, 1950)
Sad life Nash(1928-) Ph.D in Math, Princeton Univ.(1950), MIT : 1951-
59, 1959-1990 paranoid schizophrenic
Sylvia Nasar, A Beautiful Mind:a biography of John Forbes Nash,
Jr, 1998; (Film, 2001)
3) Nobel Prize in Economics in 1994
Three Game theorists, Nash, Harsanyi, and Selten won the
Nobel Memorial Prize in Economic Sciences in 1994 “for
their pioneering analysis of equilibria in the theory of
non-cooperative games”. Press Release
Complete Incomplete
Imperfect Ch 1 [Nash Equilibrium] Ch 3 [Bayesian NE]
(static) Nash, 1950-51 Harsanyi 1967-68
Perfect Ch 2 [Subgame Perfect NE] Ch 4 [Perfect Bayesian NE]
(dynamic) Selten 1965, 1975 Harsanyi 1967-68
4) applications
Auction analysis should certainly be counted as one of the
most important applications of game theory, and the FCC
auctions gave a practical demonstration of the power of
auction analysis. (Myerson, 1997, p.1078-1079)
See,
Paul Milgrom, Auction Theory for Privatization,
Cambridge, 2000,
FCC, Wireless Telecommunications Bureau Auctions
FCC Home Page
"the greatest auction in history," raising over $7 billion
for the U.S. government.