Post on 09-Jul-2020
Game Theory—Introduction
曽 道 智Zeng, Dao-Zhi
Tohoku University
April 21, 2019
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 1 / 24
Welcome to Game Theory
Time: 1st class on TuesdayGoogle Classroom (Codes anuzdcp (main), x2xiooo)Lecturer
Name: 曽道智 (ゼン・ダオズ) Zeng, Dao-ZhiMail: zeng@se.is.tohoku.ac.jp (Anytime is OK for questions!)Url: http://www.se.is.tohoku.ac.jp/̃ zeng/index.htmlMajor: Regional Science, Urban Economics, SpatialEconomics, Conflict ResolutionAspiration: Teaching knowledge worldwide applicable andfostering regional specialists with international viewpoints
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 2 / 24
Lecture plan
Date Content1st 4/21 Introduction2nd 4/28 Strategic form game3rd 5/12 Extensive form game with perfect information4th 5/19 Application examples5th 5/26 Application in imperfect competition markets6th 6/2 Mixed strategy7th 6/9 General extensive-form games 8th 6/19 Repeated games 9th 6/23 Application examples10th 6/30 Strategic form games with imperfect information11th 7/7 Bargaining game12th 7/14 Application13th 7/21 Application14th 7/28 Cooperative game15th 8/4 Test
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 3 / 24
References
Textbook渡辺隆裕, 2008: ゼミナールゲーム理論入門,日本経済新聞出版社。
Lecture 1: Chapters 1&13
References岡田章, 2011: ゲーム理論(新版),有斐閣.武藤滋夫, 2011: ゲーム理論,オーム社.
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 4 / 24
Game Theory
Game?Gambling machinehow to win?how to avoid a loss?
Game TheoryA science to explore howmultiple agents makedecisions in situations withconflicts and cooperationdescribed by games.
Nobel Laureates1994: John Nash, ReinhardSelten, and John Hasanyi2005: Thomas Schelling andRobert Aumann2007: Leonid Hurwicz, EricMaskin, and Roger Myerson2012: Alvin E. Roth andLloyd S. Shapley2014: Jean Tirole.
John Maynard Smith: theCrafoord Prize for his applicationof game theory to biology
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 5 / 24
Three components
PlayerDM(e.g.individuals, firms,governments)agentsrepresentinguncertain factors(e.g., weather) arenot DMs.rationalintelligent
StrategyAction plans made by playersIt may depend on the states.Astrategy describes how a playerchooses a specific action in everypossible state.
Payoffnumerical expression of a player’spreferencedefined for every possible outcomeof players’ strategiesanother name—utility
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 6 / 24
Game forms
matrix (prisoner’s dilemma)
Prisoner 1Prisoner 2
Silent Betray
Silent −1,−1 −10,−0.5Betray −0.5,−10 −8,−8
Graph
Teacher
Student
Student’s payoff −2 1
Teacher’s payoff −2 1
tough easy
stop continue stop Continue
−2 0−1 0
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 7 / 24
Equilibrium concept
A theoretical concept to predict plausible results of gamesdominant strategies, Nash equilibrium· · · perfect equilibrium
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 8 / 24
Rules of Games
Game rule= {Player,Strategy,Payoff}complete information
All players know the rule of the game completelycommon knowledgecomplete , perfect
Games with incomplete informationSome different Japanese terms for players,プレーヤー,プレイヤー
limited to a small number of playersrationallity: players maximize their own payoffsmechanism design
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 9 / 24
Classification of Games I
2-player game, 3-player game, n-player gamenoncooperative and cooperative games
Noncooperative games Players do not cooperate. Toinvestigate economic behavior when individual players maketheir decisions based on their own interests
zero-sum and nonzero-sum
Cooperative games Players cooperate with each other. Toanalyze how players divide the total value of a result fromcooperation in a fair wayThe forming of a coalition depends on the related players’decisionsNG theory is more basic than CG theory. Some studies focuson how s coalition is formed based on NG theory.
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 10 / 24
Classification of Games II
Games in strategic form, games in extensive form, games incoalitional form
Representative models to study games by mathematics
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 11 / 24
The History of Game Theory I
John von Neumann(1928)On the theory of games of strategyto prove the minimax theory (Brouwer’s fixed-point theorem)to formulate n-persion games in strategic form,to propose theconcept of coalitions, characteristic function based on themaximin value,to analyze zero-sum 3-person cooperativegames.
von Neumann and Morgenstern(1944)Theory of Games and Economic Behavior
John Nash(1950,1953)Nash equilibriumNash bargaining solution,Nash program
Harold W. Khun(1953)develop extensive games
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 12 / 24
The History of Game Theory II
complete information, perfect recall, behavioral strategy, andetc.the existence of a pure-strategy equilibrium in any game withperfect recallthe equivalence between behavioral strategy and mixedstrategy
Other research in 1950scooperative gameShapley value (Shapley, 1953)Core (Shapley, 1953; Gillies, 1959)The existence of a general equilibrium by Arrow and Debreu
Research in 1960sCooperative game
cooperative games without side payments(Auman and Peleg,1960; Auman, 1961)
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 13 / 24
The History of Game Theory III
Bargaining set(Auman and Maschler, 1964)Kernel(Davis and Maschler, 1965)Nucleolus(Schmeidler, 1969)The existence of a core(Bondareva, 1963; Shapley, 1967)
Noncooperative gamethe core of market games(Schubik, 1959; Debreu and Scarf,1963)subgame perfect equilibrium(Selten, 1965)Bayesian equilibrium and games with incomplete information(Harsanyi, 1967-68)
Research in 1970s and early 1980sNoncooperative game (refinement of equilibria)perfect equilibrium(Selten, 1975)sequential equilibrium(Kreps and Wilson, 1982)Repeated gamesFolk theorem(Rubinstein, 1979)
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 14 / 24
The History of Game Theory IV
Bargaining gamesnoncooperative bargaining games(Rubinstein, 1982)noncooperative bargaining model for n-player coalition games(Selten, 1981)
Research in the middle and late 1980sbounded rationalityevolutionary game theory(Maynard Smiths and Price, 1973)learning theoryadaptation, rational learning, adaptive learning
Research after 1990sBehavioral game theory (Camerer, 2003)
Social preferences, guessing game
game experimentsto explore rational behavior
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 15 / 24
von Neumann
https://commons.
wikimedia.org/wiki/File:
JohnvonNeumann-LosAlamos.gif
1903–1957. Born inHungary. Move to U.S. in1930. Died in 1957.started learning calculus atthe age of 8awarded Ph.D. inmathematics, physics,chemistry when he was 23great contribution inmathematics, physics,meteorology, economics,computer science, nucleardevelopment · · ·
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 16 / 24
Oskar Morgenstern
https://mises.org/profile/
oskar-morgenstern-0
1902–1977. Born inGermany. Passed away atPrinceton.his mother: an illegitimatedaughter of AustrianEmperor Emperor FrederickIIIAdolf Hitler took over Viennain 1938. Fired by theUniversity of Vienna andstayed in Princeton as alecturer.
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 17 / 24
John Nash
https://commons.
wikimedia.org/wiki/File:
John_Forbes_Nash,_Jr._by_
Peter_Badge.jpg
1928–2015. Born in Virginia.Taxi accident.Entered Carnegie MellonUniversity to learn Chemistrywhen he was 17. Turn toInternational EconomicsMaster degree when he was 20.Moved to Princeton for a Ph.D.Ph.D. when he was 22. Advisor:Prof. Albert William TuckerAwarded Nobel prize by 3papersA beautiful mind
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 18 / 24
A mathematical genius
https:
//www.facebook.
com/PrincetonU/
photos/a.
402851790773/
10153451228495774/
?type=3&theater
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Reinhard Selten
https://commons.
wikimedia.org/wiki/File:
Reinhard_Selten2.jpg
1930-2016. Born inGermany.Bachlor: majored inmathematics.Ph.D: experimentaleconomicsStarted game theoryresearch in 1965Contribution: extensivegames and refinement ofNash equilibriaGood at Esperanto
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 20 / 24
A photo taken at Kagawa University
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 21 / 24
John Charles Harsanyi
https://upload.wikimedia.org/
wikipedia/en/6/6b/John_
Harsanyi.jpg
1920–2000. Born inBudapest and died atBerkeley.entered chemical eng. at theU. of Lyon when he was 19.Due to the 2nd WW,returned to Hungary to studypharmacology at the U. ofBudapestBachelor when he was 24Awarded a Ph.D. when hewas 27Moved to Australia in 1950and moved to the U.S. in1960s
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 22 / 24
New Trend: Bounded rationality
Evolutionary gametheory
re-import from biologyshort-sighted action,imitationmutation, selectionreplicator dynamics,migration of skilledworkers—
Behavioral Game TheoryExperimental economicsSubjects: college studentsObserve human behaviorExamination of theory.Revise theory if necessaryFairness and altruisticbehavior
曽 道 智 Zeng, Dao-Zhi (Tohoku University) Game Theory—Introduction April 21, 2019 23 / 24
Homework
Give example(s) in which more than one people makedecisions in the real world.What is your motivation to take this course? What do youexpect from it?
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