Game Theory

(Giochi finiti e giochi differenziali)

  Game theory

• Elements of choice theory, utility functions    
• Definition of game in extensive and normal form.
• Pure, mixed, behavioural and general strategies.
• Zero sum games and minimax theorems.
• Nash equilibria and their refinements.
• Evolutionary game theory, learning and evolution.
• Special classes of games: Market games, Auction theory.

Elements of optimal control theory and differential games

• The Hamilton Jacobi Bellman equation.
• Pontriagin maximum principle.
• Viscosity solutions.
• Differential games.
• Isaacs equation.
• Explicit solutions of some differential games.

R.Meyerson, "Game Theory", Harvard Univ. Press 1991.

G. Giraud : "La theorie des jeux ", Flammarion, 2000.

K. Ritzberger, "Foundations of Non-Cooperative Game Theory", Oxford University Press.

J. Weibull, "Evolutionary Game Theory" , MIT Press 1995.

B. Sandholm, "Deterministic Evolutionary Dynamics". Forthcoming, The New Palgrave Dictionary of Economics , 2nd edition.
Available on http://www.ssc.wisc.edu/~whs/research/ded.pdf

A. von Schemde "Index and Stability in Bimatrix Games. A Geometric-Combinatorial Approach",Lecture Notes in Economics and Mathematical Systems , Springer, Berlin, 2005

V.Krishna, "Auction Theory", Academic Press 2002

M.Bardi, I.Capuzzo Dolcetta, "Optimal control and viscosity solutions of Hamilton- Jacobi- Bellman equations", Birkhauser 1997

P. Mannucci  "Nash Points for general nonzero-sum differential games"

P. Mannucci  "Nonzero-sum stochastic differential games with discontinuous feeedback", SIAM J. CONTROL OPTIM. , 2004, Vol. 43, No. 4, pp. 1222–1233 or click here

R.Isaacs, "Differential Games", Dover Publications Inc.1999

J. Lewin, "Differential Games: Theory and Methods for Solving Game Problems with Singular Surfaces", Springer, 1994.

A. Friedman,  "Differential Games", Dover Publications Inc., 2006