Ch.1. Introduction: Game and Game Theory

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Ch.1. Introduction Game and Game Theory
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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) Nashs Nash Equilibrium
• 3) Nobel Prize in economics, 1994
• 4) Applications

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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 Zermelos theorem on
  Chess(1913).
• However, game theory is no longer concerned with
  amusement games.

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 Zermelos 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.

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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)

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c) comparison.

• Games in game theory
• 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 -gt
  economics, business, sociology, politics,
  biology,

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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.
• --gt more descriptively accurate names "Conflict
  analysis" or "interactive decision theory"
  (R.B.Myerson, Game Theory analysis of conflict,
  Harvard Univ. Press, 1991, p.1)
•  
•  

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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.

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• 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 -gt 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 -gt static
  games games with a single stage

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• 3) complete information vs. incomplete
  information game
• Incomplete information at least one player is
  uncertain about another players payoff function.
  Asymmetric or private information
• Ex) Firms MC and workers ability may be
  private information.

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4)  Contents of our textbook

•  

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1.3 Evaluation of Game Theory

• 1) Rubinstein
• ("Introduction" in Game theory in
  Economics, eds by A. Rubinstein, 1990, p.xi)
• 1950s-- era of general equilibrium
• 1960s-- era of growth
• 1970sera of economics of information
• 1980s era of game theory

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2) Nashs 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.

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? Nashs 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 Minda biography of
  John Forbes Nash, Jr, 1998 (Film, 2001)

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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

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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.