An Alternate Approach to Axiomatizations of the Von Neumann/Morgenstern Characteristic Function.
Abstract
The concept of the characteristic function of a game- that gives us an intuitive idea of the value of a coalition - is of central importance in the theory of N-person cooperative games. In those cases where the players have full knowledge of the structure of a game, in the sense of knowing not only the various parameters but also the payoff functions of the other players, the value of a coalition S, denoted v(S), is defined to be the unique value of the two-person zero-sum game between S and N-S. The function thus defined satisfies two properties. The first property states that no gain will be forthcoming from non-participation. The second asserts that anything two disjoint coalitions can achieve can be achieved can be achieved by the union of the two, and possibly even more could be achieved by the latter. The characteristic function, however, does not tell us anything about the behavior of the players involved. The situation gets even more complicated if we drop the assumption that every player knows every other player's payoff function, and assume merely that he has some, not necessarily correct, perception of these. In this case, we have in addition to the true game parametrized by the true payoff functions, the game that different players perceive to exit. In the extreme case, where no player knows anybody's else's payoff function, there are new games defined, one for each of the players.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1987
- Accession Number
- ADA182642
Entities
People
- Alain A. Lewis
- Raghu Sundaram
Organizations
- Stanford University