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MarcianoSiniscalchi

Game Theory(Economics 514)
Fall 1999

Logistics

We (provisionally) meet on Tuesdays andThursdays, 10:40a-12:10p, inBendheim317.

I will create a mailing list for thecourse. Therefore, please send me email at your earliest convenience soI can add you to the list. You do not want to miss important announcements, doyou?

The course has a Web page at http://www.princeton.edu/~marciano/eco514.html.You should bookmark it and check it every once in a while, as I will be addingmaterial related to the course (including solutions to problems, papers,relevant links, etc.)

If you need to talk to me, you can email meat marciano@princeton.edu for anappointment, or just drop by during my regular OH (Wed 1:00-2:30). My office is309 Fisher.

Textbook

The main reference for this course is:

OSBORNE, M. and RUBINSTEIN, A. (1994): A Course in Game Theory, Cambridge, MA:MIT Press (denoted “OR” henceforth)

If you are planning to buy a single bookfor this course, get this one. However, I will sometimes refer to the followingtexts (which, incidentally, should be on every serious micro theorist’sbookshelf):

MYERSON, R. (1991): Game Theory. Analysis of Conflict, Cambridge, MA: HarvardUniversity Press (denoted “MY” henceforth)

FUDENBERG, D. and TIROLE, J. (1991): Game Theory,Cambridge, MA: MIT Press (denoted “FT”henceforth)

Plan of the Course

Please note: R indicates required readings;O indicates optional readings; and Lmeans that relevant lecture notes will be distributed in class. Lecture notesshall be considered requiredreadings.

1. Introduction

1.1 Themain issues
Structure of the Course
Games as Multiperson Decision Problems

R OR Chapter 1

O MY Sections 1.1-1.5

1.2 Zerosum games
Minmax theory
The Minmax theorem and LP

R ORSection 2.5

L

2. Normal—Form Analysis

2.1 Beliefs and BestResponses
Dual characterizations of Best Responses

Iterating the“best response operator:” rationalizability, iterated weak dominance.

R OR Section 2.1 and Chapter 4

O MY Sections 1.8 and 3.1;

BERNHEIM,D. (1984): “Rationalizable Strategic Behavior,” Econometrica,

52, 1007-1028.

2.2 Fixedpoints of the best response operator: Nash equilibrium.

Existence andmixed strategies. Interpretation.

R OR Sections 2.2-2.4 and 3.1-3.2

3. Games withIncomplete Information

3.1 Thebasic model

The Harsanyiapproach

Bayesian NashEquilibrium. Interpretation.

R OR Section 2.6

3.2 Acloser look: higher-order beliefs
Common Priors

L

4. InteractiveBeliefs and the Foundations of Solution Concepts

4.1 The basic idea:Harsanyi’s model revisited
Correlated Equilibrium

R ORSection 3.3

L

4.2 Rationality andthe Belief operator
Common Certainty of Rationality.

Equilibrium inBeliefs.

L

O DEKEL, E. and GUL, F. (1990): “Rationality and Knowledge inGame Theory,”

in Advances in Economicsand Econometrics, D. Kreps and K. Wallis, eds.,

Cambridge University Press,Cambridge, UK;

TAN, T.C.C. andWERLANG, S.R.C. (1988): “The Bayesian Foundations of Solution Concepts ofGames,” Journal of Economic Theory,45, 370-391.

AUMANN, R. andBRANDENBURGER, A. (1995): “Epistemic Conditions for Nash Equilibrium,” Econometrica, 63, 1161-1180.

5. Putting it All Together: SomeAuction Theory

5.1 First- and Second-priceauctions
Dominance and Equilibrium analysis with private values
The Revenue Equivalence Theorem

LO MY Section 3.11

5.2 Rationalizabilitywith Incomplete Information
Non-equilibrium analysis of auctions
Computation!

L

6. ExtensiveGames: Basics

6.1 Extensivegames with perfect information

Notation(s) andterminology

Nash equilibrium

R OR Sections 6.1, 6.3, 6.4

6.2 Backward Induction andSubgame-Perfect equilibrium
The One-Deviation Property

Extensive gameswith perfect but incomplete information

Perfect Bayesianequilibrium

R OR Section 6.2, 12.3 up to p. 233