Cooperative games Syllabus A selective course for Faculty of Computer Science Applied Mathematics and Information Science Bachelor's Program Cooperative game theory is the essential and chronologically original component of modern game theory. Its key idea is to study conflicts by analyzing the abilities of possible player coalitions, disregarding the exact mechanics of coalition formation, intra-coalition bargaining and player strategic actions. This provides robust and strict approach to studying games where exact non-cooperative formalization via strategies and payoffs is too complex, unconvincing or problematic in some other way. Classical and by-far most famous application of this approach is market exchange model in general equilibrium economics. The course focuses on applications of cooperative games in market equilibrium theory, mechanism design and networks. Course requires basic game theory, basic microeconomics, calculus, linear algebra, probability and discrete math. Course Plan 1. Introduction to cooperative games. Transferable and nontransferable utility, core, Shapley value, other solution concepts. Axiomatic characterization. Implementation. 2. Market games, core property of competitive equilibrium. 3. Cooperative games in local public good economies. 4. Cooperative games and market design. Matchings and other applications. 5. Cooperative games on networks. Main textbooks 1. Michael Maschler, Eilon Solan, Shmuel Zamir. Game theory. Cambridge University Press. 2013. 2. Peleg B., Sudholter P. Introduction to the theory of cooperative games. Kluwer Acad. Publiushers, 2003 3. H. Peters, Game theory. A multi-leveled approach, Springer, 2008. 4. H. Moulin, Axioms of cooperative decision making, Econometric Society Monographs Series, Cambridge University Press, 1988. 5. The Shapley value. Essays in honor of Lloyd S. Shapley. Edited by Alvin E. Roth, Cambridge University Press, 1988. 6. Mas-Colell A., Whinston M. D., Green J. R. Microeconomic Theory. Oxford University Press, 1995. 7. Roth, Alvin E. and Marilda Sotomayor, Two-Sided Matching: A Study in Game-Theoretic Modelling and Analysis, Econometric Society Monograph Series, Cambridge University Press, 1990. 8. Scotchmer, S., Local Public Goods And Clubs. Handbook of Public Economics, Volume 4, 2002. Grading System 50% homework, 50% final exam.
