Classical Cooperative Theory I: Core-Like Concepts

Pure bargaining games discussed in the previous two lectures are a special case of n-person cooperative games. In the general setup coalitions other than the grand coalition matter as well. The primitive is the coalitional form (or, “coalitional function”, or “characteristic form”). The primitive can represent many different things, e.g., a simple voting game where we associate to a winning coalition the worth 1 and to a losing coalition the worth 0, or an economic market that generates a cooperative game. Von Neumann and Morgenstern (1944) suggested that one should look at what a coalition can guarantee (a kind of a constant-sum game between a coalition and its complement); however, that might not always be appropriate. Shapley and Shubik introduced the notion of a C-game (see Shubik (1982)): it is a game where there is no doubt on how to define the worth of a coalition. This happens, for example, in exchange economies where a coalition can reallocate its own resources, independent of what the complement does.

[1]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[2]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[3]  John C. Harsanyi,et al.  A Simplified Bargaining Model for the n-Person Cooperative Game , 1963 .

[4]  Lloyd S. Shapley,et al.  The Shapley value: Utility comparison and the theory of games , 1967 .

[5]  W. F. Lucas,et al.  A Game with No Solution , 1968 .

[6]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

[7]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[8]  M. Shubik.  Game theory in the social sciences: Concepts and solutions , 1982 .

[9]  H. Young.  Monotonic solutions of cooperative games , 1985 .

[10]  Sergiu Hart,et al.  An axiomatization of Harsanyi's nontransferable utility solution , 1985 .

[11]  Bezalel Peleg,et al.  An axiomatization of the core of cooperative games without side payments , 1985 .

[12]  Robert J. Aumann,et al.  AN AXIOMATIZATION OF THE NON-TRANSFERABLE UTILITY VALUE , 1985 .

[13]  Hans Keiding.  An axiomatization of the core of a cooperative game , 1986 .

[14]  E. Packel.  Game Theory in the Social Sciences Concepts and Solutions (Martin Shubik) , 1987 .

[15]  B. Peleg.  On the reduced game property and its converse , 1987 .

[16]  L. Shapley.  A Value for n-person Games , 1988 .

[17]  Lloyd S. Shapley,et al.  Utility comparisons and the theory of games , 1988 .

[18]  G. Owen,et al.  The consistent Shapley value for hyperplane games , 1989 .

[19]  A. Mas-Colell.  An equivalence theorem for a bargaining set , 1989 .

[20]  S. Hart,et al.  Potential, value, and consistency , 1989 .

[21]  Sergiu Hart,et al.  Advances in Value Theory , 1990 .

[22]  T. Ichiishi,et al.  Game Theory and Applications , 1990 .

[23]  Bezalel Peleg,et al.  Axiomatizations of the core , 1992 .

[24]  William F. Lucas,et al.  Von Neumann-Morgenstern stable sets , 1992 .

[25]  G. Owen,et al.  The Consistent Shapley Value for Games without Side Payments , 1992 .

[26]  M. Maschler.  The bargaining set, kernel, and nucleolus , 1992 .