A Value for n-Person Games

A Value for n-Person Games is a foundational text in game theory and cooperative game analysis. The book introduces what became known as the Shapley value - a solution concept for fairly allocating gains and costs among players in coalition games. Shapley presents mathematical formulas and axioms that determine how to distribute payoffs when multiple parties can form different collaborative arrangements. The work demonstrates these principles through examples involving voting power, cost allocation, and market situations. The mathematical framework builds systematically from two-person to n-person scenarios, establishing properties like efficiency, symmetry, and additivity. Key proofs and derivations show how the Shapley value emerges as the unique solution satisfying these core requirements. The concepts in this book underpin modern approaches to bargaining theory, fair division problems, and cooperative game solutions across economics and political science. The work connects abstract mathematical principles to practical questions of fairness and stability in group decision-making.

There are not enough internet reviews to create a summary of this book. Instead, here is a summary of reviews of Lloyd Shapley's overall work: Note: Lloyd Shapley published academic papers and mathematical works rather than books for general readers, so traditional reader reviews are limited. His work is primarily discussed in academic contexts. Academic readers value Shapley's clear mathematical proofs and elegant solutions to complex allocation problems. His papers on cooperative game theory receive citations for their precise formulations and practical applications. Several researchers note how his Shapley value concept provides intuitive solutions to fair division problems. PhD students and researchers sometimes find his papers challenging due to dense mathematical notation and assumptions of advanced knowledge. Some note that additional explanatory material would help accessibility. On Google Scholar, his most-cited works include: - "College Admissions and Stability of Marriage" (23,000+ citations) - "On Cores and Indivisibility" (3,000+ citations) - "Values of Large Games" (2,800+ citations) Traditional review sites like Goodreads and Amazon do not have ratings for Shapley's academic publications. His work appears primarily in economics journals and mathematical proceedings.

Theory of Games and Economic Behavior by John von Neumann, Oskar Morgenstern This foundational text explores game theory's mathematical principles and their applications to economic behavior, building on concepts that Shapley later developed.

Games and Decisions by R. Duncan Luce and Howard Raiffa The text presents mathematical approaches to decision-making and game theory with applications in social sciences and economics.

Contributions to the Theory of Games by Harold Kuhn and Albert Tucker This collection contains mathematical papers on game theory that complement Shapley's work on cooperative games and coalition formation.

Game Theory: Analysis of Conflict by Roger B. Myerson This mathematical treatment covers both cooperative and non-cooperative game theory with emphasis on economic applications and solution concepts.

A Course in Game Theory by Martin J. Osborne, Ariel Rubinstein The book provides mathematical foundations of game theory with focus on economic applications and strategic behavior analysis.

🎲 Lloyd Shapley's paper "A Value for n-Person Games" (1953) revolutionized game theory and earned him the Nobel Prize in Economics nearly 60 years later in 2012. 🔍 The Shapley value, introduced in this work, provides a unique solution for fairly distributing both gains and costs among several actors, and is now used in everything from voting power analysis to internet routing costs. 💡 While Shapley wrote this breakthrough paper at RAND Corporation, he was initially hired there to help calculate radiation dispersal patterns for nuclear weapons - his game theory work was a side project. 🤝 This mathematical concept has found surprising applications in modern technology, including determining fair compensation for data sharing in machine learning and artificial intelligence systems. 📚 Though published as part of the small book "Contributions to the Theory of Games, Volume II," this single chapter has been cited over 20,000 times and spawned multiple fields of research in economics, political science, and computer science.