COMPOUND SIMPLE GAMES, III: ON COMMITTEES
Abstract
This is an investigation of the structural properties of those multi- person games, called 'simple', in which every coalition either can win outright or is completely defeated. The central idea is the concept of a 'committee', which may be characterized roughly as a set of players whose internal politics are independent of the rest of the game. The possible relationships between different committees in the same game are explored: co-existing committees may be disjoint and independent, or one committee may contain another; but only under special circumstances can two committees overlap without inclusion. The principal result is to establish that every simple game can be decomposed into a hierarchy of 'prime' games (i.e., committee-free games), in which the player- positions are filled either by individual players or by other prime games or sums or products thereof, and that this decomposition is essentially unique.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1967
- Accession Number
- AD0660550
Entities
People
- Lloyd Shapley
Organizations
- RAND Corporation