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.
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