A01=Alan D. Taylor
A01=William S. Zwicker
Addition
Ambiguity
Antichain
Author_Alan D. Taylor
Author_William S. Zwicker
Automorphism
Big O notation
Bijection
Binary relation
Boolean function
Category=PBUD
Characteristic function (probability theory)
Coefficient
Combination
Combinatorial proof
Comparability
Complement (set theory)
Conjecture
Contradiction
Convex combination
Convex hull
Cooperative game
Counterexample
Diagram (category theory)
Disjoint sets
Disjoint union
Dot product
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equal Weight
Existential quantification
Hypergraph
Hyperplane
Inequality (mathematics)
Infimum and supremum
Integer
Intersection (set theory)
Intransitivity
Linear independence
Linear inequality
Lowest common denominator
Magic square
Mathematical induction
Monotonic function
Natural number
Natural transformation
Negation
Pairwise
PAQ
Partially ordered set
Permutation
Power set
Pullback (category theory)
Rational point
Real number
Restriction (mathematics)
Result
Set (mathematics)
Shapley value
Special case
Subset
Substructure
Summation
Superadditivity
Surjective function
Theorem
Threshold graph
Total order
Transferable utility
Transitive relation
Ultrafilter
Unordered pair
Weight function
Weighting
Without loss of generality
Product details
- ISBN 9780691001203
- Weight: 510g
- Dimensions: 152 x 235mm
- Publication Date: 12 Oct 1999
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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Simple games are mathematical structures inspired by voting systems in which a single alternative, such as a bill, is pitted against the status quo. The first in-depth mathematical study of the subject as a coherent subfield of finite combinatorics--one with its own organized body of techniques and results--this book blends new theorems with some of the striking results from threshold logic, making all of it accessible to game theorists. Introductory material receives a fresh treatment, with an emphasis on Boolean subgames and the Rudin-Keisler order as unifying concepts. Advanced material focuses on the surprisingly wide variety of properties related to the weightedness of a game. A desirability relation orders the individuals or coalitions of a game according to their influence in the corresponding voting system. As Taylor and Zwicker show, acyclicity of such a relation approximates weightedness--the more sensitive the relation, the closer the approximation. A trade is an exchange of players among coalitions, and robustness under such trades is equivalent to weightedness of the game.
Robustness under trades that fit some restrictive exchange pattern typically characterizes a wider class of simple games--for example, games for which some particular desirability order is acyclic. Finally, one can often describe these wider classes of simple games by weakening the total additivity of a weighting to obtain what is called a pseudoweighting. In providing such uniform explanations for many of the structural properties of simple games, this book showcases numerous new techniques and results.
Alan D. Taylor is the Marie Louise Bailey Professor of Mathematics at Union College. William S. Zwicker is Professor of Mathematics at Union College. Both have taught at Union for twenty-four years; their research has been in the areas of combinatorial set theory and applications of mathematics to political science, including social choice theory, fair division, and game theory.
