ch1

							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.