Suchergebnisse

In this paper, we study committee decision making process using game theory. By a committee, we mean any group of people who have to pick one option from a given set of alternatives. A well defined voting rule is specified by which the committee arrives at a decision. Each member has a preference relation on the set of alternatives. A new solution concept called the one-core in introduced and studied. Intuitively, the one-core consists of all maximal (for the proposer) proposals which are undominated assuming that the player who makes the proposal does not cooperate in any effort to dominate the proposal. For games with non-empty cores, the one-core proposals are shown to be better than the core. For games with empty cores, the one-core proposals tend to be pessimistic, i.e., they indicate the security levels of the players. This is because the stability requirements of the one-core are too strong for such games. A bargaining set modeled along the lines of the Aumann-Maschler bargaining set for characteristic function games is defined for committee games. Because of its relaxed stability requirements, the bargaining set indicates more reasonable proposals than the one-core. The existence of both the one-core and the bargaining set are studied and these concepts are compared with two other well known solution concepts--the core and the Condorcet solution.

We describe a framework and an algorithm for approximately solving a class of hybrid influence diagrams (IDs) containing discrete and continuous chance variables, discrete and continuous decision variables, and deterministic conditional distributions for chance variables. A conditional distribution for a chance variable is said to be deterministic if its variances, for each state of its parents, are all zeroes. The solution algorithm is an extension of Shenoy's fusion algorithm for discrete influence diagrams. To mitigate the integration and optimization problems associated with solving hybrid IDs, we propose using mixture of polynomials approximations of conditional probability density and utility functions and piecewise linear approximations of nonlinear deterministic conditional distributions for continuous chance variables. The class of hybrid IDs that can be solved by our framework are those that do not involve divisions. The framework and algorithm are illustrated by solving two small examples of hybrid IDs.