Simple Games (eBook)

Desirability Relations, Trading, Pseudoweightings

Alan D. Taylor, William S. Zwicker (Autoren)

eBook Download: PDF

2021
Princeton University Press (Verlag)
978-0-691-22389-6 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 12.1.2021
• Zusatzinfo: 47 line illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Allgemeines / Lexika
• Schlagworte: abstention • Addition • adiabatic computing • adjacency of vertices • alternating cycle • Ambiguity • Antichain • ANTISYMMETRY • augmented trading matrix • automorphic coalitions • automorphism • balanced game • Basic Class • bicameral join • bicameral meet • Big O notation • bijection • Binary Relation • B-medium coalition • boolean function • Boolean subgame • canadian system • Cardinality • Cartesian Product • characteristic function form • Characteristic function (probability theory) • Chow games • Chow parameters • classification of linear games • classified coalition • coefficient • column union • combination • combinatorial proof • Comparability • Complement (set theory) • complement symmetric relation • compound simple game • conjecture • constant-sum games • Contradiction • convex combination • convex hull • convex set • Cooperative Game • count and account method • counterexample • diagonal • Diagram (category theory) • Dimension theory (algebra) • direct market • Disjoint sets • Disjoint union • dot product • double appearance • downward closure • dual game • dual property • edge, of a graph • EL-sequence • Equal Weight • equivalence class • existential quantification • fair division • Finite set • Gabelman game • geometry of simple games • grant of certiorari • Hahn-Banach theorem • Harvard Band • high failure • homogeneous games • Hypercube • Hypergraph • hyperplane • identification of variables • Identity function • imaginary number • Inequality (mathematics) • Infimum and supremum • Integer • Intersection number (graph theory) • Intersection (set theory) • Interval Game • INTRANSITIVITY • k-asuramability • large coalition • Linear combination • linear games • linear graph • Linear Independence • Linear Inequality • Line segment • losing coalition • Lowest common denominator • Luxembourg • Magic Square • Main diagonal • major player • master player • Mathematical Induction • mathematical structure • Mathematics • Matrix addition • Monotonic Function • monotonicity • multipartition • multiweighting • Natural number • Natural transformation • Negation • pairwise • PAQ • partially ordered set • Permutation • Power set • pullback • Pullback (category theory) • Rational number • Rational point • real number • rectangle • Restriction (mathematics) • result • Robustness • Sequence • Set (mathematics) • Shapley Value • small number • Special case • SUBGROUP • Subset • Substructure • Summation • Superadditivity • Surjective function • Symmetric group • Theorem • theory • Threshold graph • Total order • transferable utility • Transitive relation • Tuple • Ultrafilter • uniqueness • Unordered pair • Vector Space • Weighted voting • Weight function • weighting • Without loss of generality
• ISBN-10: 0-691-22389-0 / 0691223890
• ISBN-13: 978-0-691-22389-6 / 9780691223896