February 16, 2012, GIRV 2110

Recent developments in networked multi-agent systems have revived interest in game theory and its underlying paradigms. The central questions originate from the interplay amongst rationality, information and conflict. Although the management of real-life networks involves complex dynamic systems, an introductory understanding of the key conceptual issues does not require but the simple, highly abstract models provided by static or repeated matrix games. This series of lectures will focus on a few selected topics, possibly complementing currently offered GT classes with emphasis on scope, assumptions, solution concepts, algorithms and open problems. The following will be covered in the course: 1. Individual vs Collective rationality 2. Knowledge and Common Knowledge 3. Equilibrium, Best-reply, Expectations 4. Time consistency, Perfectness, Dynamic Programming 5. Incomplete Information and Learning 6. Bargaining READING MATERIAL Reference book A1) A modern outlook on multi-agent systems: Yoav Shoham, Kevin Leyton-Brown. Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2009 B1) A classic reference for control engineers: T. Basar, Older G.J., Dynamic Non-cooperative. Game Theory, Academic Press. Common knowledge, Equilibrium Instructive puzzles: http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle http://en.wikipedia.org/wiki/Guess_2/3_of_the_average http://en.wikipedia.org/wiki/Pirate_game A2) The seminal paper: B. Aumann, Backward Induction and Common Knowledge of Rationality, Games and Economic Behaviour, 8-1995, pp. 6-19 http://www.ma.huji.ac.il/raumann/pdf/36.pdf B2) A recent formalization: D. A. Novikov, Models of Reflexive Collective Behavior, 18th IFAC World Congress, Milano,it, 2011 C2) Philosophical overtones: P. Caravani, On Voluntariness of Nash Equilibrium, Proc. Game Theory and Management, St. Petersburg 2011 Learning A3) Historic paper: Kumpati S. Narendra, M. A. L. Thathachar, Learning Automata: A Survey. IEEE Transactions On Systems, Man, And Cybernetics, Vol. smc-4, No. 4, July 1974 B3) Seminal in Equilibrium Learning: P. S. Sastry, V. V. Phansalkar, M. A. L. Thathachar, Decentralized Learning of Nash Equilibria in Multi-Person Stochastic Games With Incomplete Information. IEEE Transactions On Systems, Man, And Cybernetics, Vol. 24, No. 5, May 1994 C3) On best-reply dynamics: Potential Games, Dov Monderer Lloyd S. Shapley. Games And Economic Behavior 14, 124–143 (1996). Article No. 0044 D3) Updated survey on Learning Automata: M. A. L. Thathachar, P. S. Sastry, Varieties of Learning Automata: An Overview. IEEE Transactions On Systems, Man, And Cybernetics—Part B: Cybernetics, Vol. 32, No. 6, December 2002 E3) Mixed strategy learning: F.A. Dahl, The lagging anchor model for game learning—a solution to the Crawford puzzle, Journal of Economic Behavior& Organization. Vol. 57 (2005) 287–303 Bargaining A4) Mayank Kumar, Tushar Chaudhary, Nash Bargaining Solutions (lecture notes, 2002) http://www.cse.iitd.ernet.in/~rahul/cs905/lecture15/index.html

The author is associate professor at the Electrical and Information Engineering Department of the University of L'Aquila, Italy. His interests are in the area of constrained control, dynamic games, learning automata, optimization and applications in Economics.