Hafta 114–20 Eyl
Giriş: control theory ve differential games
Introduction and course description This course will cover selected topics at the frontier of research focusing on control theory, differential games, and complementarity and supermodularity in economic theory. The prerequisites are the macro courses as well as some familiarity with continuous-time and discrete-time dynamic optimization. Because of this, the students are encouraged to look at these references: Stokey, N. and R. E. Lucas, Jr. (1989), ”Recursive methods in Economic Dynamics”, Harvard University Press. Beavis B. and I. Dobbs (1990), ”Optimization and Stability Theory for Economic Analysis”, Cambridge University Press. Gandolfo, G. (1995), ”Economic Dynamics”, 3rd. ed., Springer-Verlag, Berlin.
control theorydifferential gamescomplementaritysupermodularity
Hafta 221–27 Eyl
Kontrol teorisi ve dinamik oyunlara giriş
Part I - Control Theory and Dynamic Games The main references for the first part of the course are: Dockner, E. J., Van Long, N., Sorger, G. and S. Jørgensen (2000), ”Differential Games in Economics and Management Science”, Cambridge University Press. Basar, T. and G.J. Olsder (1999), ”Dynamic Noncooperative Game Theory”, SIAM, Academic Press, 2nd edition. [1]. Introduction: Basic concepts of game theory (a) Axioms of game theory (b) Game theoretic models (c) Dynamic games
control theorydynamic gamesgame theoretic modelsBasar & Olsder
Hafta 328 Eyl – 4 Eki
Kontrol kuramı yöntemleri ve optimal kontrol
[2]. Control theoretic methods (a) The Hamilton-Jacobi-Bellman equation (b) Pontryagin’s maximum principle (c) Information, commitment, and strategies (d) Infinite time horizon (e) Conditions for non-smooth problems
Hamilton-Jacobi-Bellman equationPontryagin's maximum principleinfinite time horizonnon-smooth problems
Hafta 45–11 Eki
Eşzamanlı oyunda Markovian equilibria
[3]. Markovian equilibria with simultaneous play (a) The Nash equilibrium (b) Equilibrium conditions (c) Time consistency and subgame perfectness
Nash equilibriumequilibrium conditionstime consistencysubgame perfectness
Hafta 512–18 Eki
Hiyerarşik oyunlar: Cournot ve Stackelberg
[4]. Differential games with hierarchical play (a) Cournot and Stackelberg equilibria in one-shot games (i) The one-shot Cournot duopoly game (ii) The one-shot Stackelberg duopoly game (iii) Introduction to time inconsistency of Stackelberg equilibria (b) Open-loop Stackelberg equilibria (c) Non-degenerateMarkovian Stackelberg equilibria
Cournot duopolyStackelberg duopolytime inconsistencyopen-loop Stackelberg equilibria
Hafta 619–25 Eki
Özel yapılı differential games
[5]. Differential games with special structures (a) Linear quadratic games (b) Linear state games (c) Exponential games
linear quadratic gameslinear state gamesexponential games
Hafta 726 Eki – 1 Kas
Stochastic differential games ve white noise
[6]. Stochastic differential games (a) Piecewise deterministic games (i) A piecewise deterministic control model (ii) Stationary Markovian Nash equilibria (iii) Piecewise open-loopNash equilibria (b) Differential games with white noise (i) A control problem with white noise (ii) Markovian Nash equilibria
piecewise deterministic gamesstationary Markovian Nash equilibriapiecewise open-loop Nash equilibriawhite noise
Hafta 82–8 Kas
Capital accumulation games ve denge stratejileri
[7]. Capital accumulation games (a) The structure of capital accumulation games (b) Qualitative properties of equilibrium strategies (c) Stability properties of equilibria (d) Games without adjustment costs (e) Knowledge as a public good
equilibrium strategiesstability of equilibriaadjustment costsknowledge as a public good
Hafta 99–15 Kas
Kaynak ve çevre ekonomisinde differential games
[8]. Differential games in resources and environmental economics (a) Non-renewable resources (i) The cooperative case (ii) The non-cooperative case (b) Non-renewable resources: some variations (i) The doomsday problem (ii) Stock-dependent utility (c) Renewable resources (i) A fishery model (ii) A fishery model with capacity constraints
non-renewable resourcesdoomsday problemstock-dependent utilityfishery model
Hafta 1016–22 Kas
Genel tekrar: Birinci bölüm
Recap: Part I
recap
Hafta 1123–29 Kas
Complementarity ve supermodularity teorisi
Part II - Complementarity and Supermodularity in Economic Theory The main references for the second part of the course are: Cooper W. R. (1999), ”Coordination Games”, Cambridge University Press Topkis (1998), ”Supermodularity and Complementarity”, Princeton University Press [1]. Pareto-Edgeworth Complementarity (a) Individual decision problems (b) Cardinal complementarity (c) The need of ordinal complementarity
Pareto-Edgeworth complementaritycardinal complementarityordinal complementarityTopkis
Hafta 1230 Kas – 6 Ara
Optimal çözümlerin duyarlılığı ve monotone comparative statics
[2]. Sensitivity solutions of optimal solutions (a) Monotone comparative statics on the real line (b) Monotone comparative statics on the plane (c) Complementarity on posets which are not the product of chains (d) Monotone comparative statics on lattices
monotone comparative staticscomplementarityposetslattices
Hafta 137–13 Ara
Supermodular ve quasisupermodular oyunlar
[3]. Supermodular and Quasisupermodular Games (a) The best reply of a quasisupermodular game (b) Tarski-Zhou fixed point theorem (c) The structure of the Nash set (d) Extensions and applications
best replyTarski-Zhou fixed point theoremNash setquasisupermodular games
Hafta 1414–20 Ara
Genel tekrar: İkinci bölüm
Recap: Part II
recap