14.12 Gam e TheoryProfessor: Muh amet Yildiz ([email protected], office hours: M 4:00-5:30, E52-251a)TAs: Eric Moos ([email protected], office hours: TBD) & Youngjin Hwang (y [email protected],office hours: TBD, E51-090)Place: E51-085 (The classroom may be c hanges in the future; check the homepage.)Time: MW 2:30-4:00.Re citation: F 10 or F 3, at E51-085.Home-page: http :// web.mit.edu /1 4.12/ w w w / inde x.htmlGam e Theory is a misnomer for Multiperson Decisio n Theory, the ana ly-sisofsituationsinwhichpayoffs to agents depend on the beha vior of otheragen ts. It involves the analysis of conflict, cooperation, and (tacit) commu-nication. Game theory has applications in sev eral fields, such as economics,politics, law, biology, and com pu ter science. In this course, I will introducethe basic tools of game theoretic analysis. In the process, I will outline someof the man y applications of game theory, primarily in economics and politicalscience.Gam e Theory has emerged as a branc h of mathematics and is still quitemathematical. Our empha sis will be on the conceptu al analysis, keepin g thelev el of math to a m inimum, especially at a level that should be quite ac-ceptab le to the a verage M IT student. Yet bear in mind that this still impliesthat you should be at ease with basic probability theor y and calculus, andmore importantly, you should be used to thinking in mathematical terms.In term ed iate Microeconomics is also a prerequisite (simultaneous attendanceto one of the in termediate courses is also acceptable). In any case, if you are1taking this course, y ou should be prepared to work hard.Text b o o k The main textbook will beRobert Gibbons, Game Theory For Applie d Economists, Prin ce-ton University Press, 1992.This is the only required textbook and cov er s the majority of this course’stopics. I recommen d that you buy it. The bookPrajit Dutta, Str ategies and Games,1999will also be ve ry useful, especially for the exercises. (You need to solve a lotof problems to learn Gam e Theory.) I will also refer toDa vid Kreps, A Course in M icro ec onom ic Theory, 1990, Har-vester.The last two books will be on reserve at Dewey; y ou are not required to buyit. All the lectures will be supplemen ted with detailed notes as well.Those who w a nt more advanced treatmen t should look at Drew Fuden-bergandJeanTirole,Game The ory, M IT Press, 1991 or Martin Osborneand Ariel Rubinstein, A Course in Game Theory, MIT Press, 1994. Thesetwobooksareverygoodbutharderthanthelevelatwhichthecourseispitc hed. Th ose who need an easier – and longer – exposition of the topicscan read Avinash Dixit and Susan Sekeath, Games of Str ategy, 2000. Therehav e been several textbooks pub lished recen tly, e.g., Joel Watson, Strategy.I encourage y o u to look at these books for extra problems to solve .Grading Ther e will be two m idterms and a compreh en sive final exam.ALL EXAMS WILL BE OPEN BOOK. Also appro ximately 5 problem sets2to be handed in.1Eac h midterm is worth 25%, the final is worth 40% , andthe prob lem sets will make up the rem aining 10% of the final grade. The firstmidterm will be on October 9th and the second one on No vem ber 13th. ThefinalexamwillbeonDecember4th. (Therewillbetwomorelecturesafterthe fina l.) A portion of the last class before each exam w ill be devoted toproblem solving and the review of the material. (The dates for these reviewsessions are October 7th, No vem ber 6th, and December 2nd.)In addition, there w ill be in-class quizzes. In these quizzes you will beasked to play various games. In m ost of these games you will not know whothe other pla yers are. Th e points (normalized to 5%) you get in these gameswill be bon u ses. They will be added to your final grade after the cut offvalues for the letter grades are determined. (In this way, y ou will not begiven any incentiv e to care about the other players’ pa yoffsinthegame.)Course Outline The following is a rough outline. Depending on the in-terests and the inclinations of the group, the topics and their weigh t m a yc h ange a little. Th e number in square brackets denotes the expected time tobe devoted to each topic. G . refers to Gibbons’ textbook.1. Introduction to game theory [1 lecture]2. Pay offs in games: Rational Choice Under Uncertaint y [1 lecture](a) Expected Utilit y Theory; Risk a version, K reps, Chapters 3.1-3.3(b) Applications; risk sharing, insurance, option value.3. A M ore Formal In troduction to Gam es [3 lectures](a) Extensive Forms and Normal Forms, G., Ch. 1.1A and 2.1A(b) Stra tegies, Dom in ant Strategies and Iterative elimination of strictlydom inated strategies, G. 1.1B1The ten tative due dates for the homew orks are 9/18, 10/2, 10/23, 11/6, and 11/27.The exact due date for each homework will be indicated on the problem set.3(c) Nash E q u ilibr iu m, G. 1.1 C(d) Applications of Nash Equilibrium, G. 1.24. Backward Induction, Subgame P erfection, and Forward Induction [3lectures](a) Analysis of Extensive-Form Games, G. 2.1A(b) Bac kward induction(c) Subgame P erfection, G. 2.2A(d) A p plication s, G. 2.2B,C,D and 2.1B,C.(e) Ba rga inin g and negotiations, G. 2.1D(f) Forward induction.(g) Applications.5. The First Midterm6. Repeated Games and Cooperation [2 lectures] G . 2.37. Incom p lete Information [2 lectures](a) B ay esian Nash Equ ilib riu m , G., 3.1A,C(b) A u ctio ns(c) A p p lication s, G. 3.28. Dy nam ic Ga m es of Incom plete Inform ation [2 lectures](a) Perfect Bayesia n Equilibrium, G. 4.1(b) Sequ ential B argain ing Under Asym m etric Information, G. 4.3B9. The second Midterm10. R epu tatio n, G. 4.3C [1 lecture]411. Pro blem s of Asymm etric Information in Economics [3 lectures](a) Sign alin g and the In tuitive Criterion, G. 4.2A and 4.4(b) Applications of Signaling, G. 4.2B,C(c) The principal-agent problem , Kreps Chapter 17(d) Applications; lemons, efficiency wages, credit-rationing, price-discrim ina tion .12. Final Exam13. E volutionary foundation s of equilibrium; ev olut ionarily stable strate-gies and replicator dyn am ics. [2