Profile Major Works Resources

Lloyd S. Shapley, 1923- 

Lloyd Stowell Shapley is mathematician at UCLA and a pioneer of game theory. 

Shapley introduced the concepts of the "core" (1953, alongside Gillies) and the "Shapley value" (1953) as solutions to coalitional cooperative games, including the value-equilibrium existence theorem (with Aumann, 1974) and the disturbing possibility of slow convergence (1975). He is perhaps most famous today for his matching theory (with Gale, 1962) and assignment problems (with Scarf, 1974).  Shapley is also credited with the 'folk theorem' of repeated non-cooperative games (and the notion of subgame perfection, with Aumann, 1976) and strategic market games (with Shubik, 1977, a frequent co-writer).

Lloyd S. Shapley shared the Nobel memorial prize in 2012 with Alvin E. Roth "for the theory of stable allocations and the practice of market design"

 

  

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Major Works of Lloyd S. Shapley

  • "A Simple Three-Person Poker Game", with J.F. Nash, 1950, Annals of Mathematical Studies.
  • "Basic Solutions of Discrete Games", with R.N. Snow, Annals of Mathematical Studies.
  • "Quota Solution of N-Person Games", 1953, Annals of Mathematical Studies.
  • "Stochastic Games", 1953, Proceedings of the NAS.
  • "Positional Games", 1953, Proceedings of Fourth Annual Logistics Conference.
  • "A Value for N-Person Games", 1953, in Kuhn and Tucker, editors, Contributions to the Theory of Games.
  • "Games with Partial Information", with H.E.Scarf, 1957, in Annals of Mathematical Studies.
  • "On Games of Survival", with J.W. Milnor, 1957, in Drescher, editor, Contributions to the Theory of Games, III
  • "Equilibrium Points in Games with Vector Payoffs", 1959, NRLQ.
  • "The Solutions of a Symmetric Market Game", 1959, in Luce and Tucker, editors, Contributions to the Theory of Games.
  • "Simple Games: An outline of the descriptive theory", 1962, Behavioral Science.
  • "Values of Games with Infinitely Many Players", 1962, Recent Advances in Game Theory.
  • "College Admissions and the Stability of Marriage", with David Gale, 1962, American Mathematical Monthly [pdf]
  • "Solutions to Compound Simple Games", 1964, Annals of Mathematical Studies.
  • "Some Topics in Two-Person Games", 1964, Annals of Mathematical Studies.
  • "Values of Large Games, VII: A general exchange economy with money", 1964, Rand.
  • Values of Non-Atomic Games, with R.J. Aumann, 1964.
  • "Quasi-Cores in a Monetary Economy with Non-Convex Preferences", with M. Shubik, 1966, Econometrica. [cwls]
  • "On Balanced Sets and Cores", 1967, NRLQ.
  • "Concepts and Theories of Pure Competition", with M. Shubik, 1967, in Shubik, editor, Essays in Mathematical Economics.
  • "Ownership and the Production Function", with M. Shubik, 1967, QJE. [cwls]
  • "On Solutions that Exclude One or More Players", 1967, in Shubik, editor, Essays in Mathematical Economics.
  • "Utility Comparison and the Theory of Games", 1969, La Decision.
  • "Pure Competition, Coalitional Power and Fair Division", with M. Shubik, 1969, IER. [cwls]
  • "On Market Games", with M. Shubik, 1969, JET. [cwls]
  • "On the Core of an Economic System with Externalities" with M.Shubik, 1969, AER.
  • "Price Strategy Oligopoly with Product Variation" with M.Shubik, 1969, Kyklos. [cwls]
  • "Cores of Convex Games", 1971, Int Journal of Game Theory.
  • "The Assignment Game, I: The core" with M.Shubik, 1972, Int Journal of Game Theory.
  • "Let's Block Block", 1972, Rand.
  • "On Balanced Games without Side Payments", 1973, in Hu and Robinson, editors, Mathematical Programming.
  • "On Cores and Indivisibility", with H.E. Scarf, 1974, JMathE.
  • Values of Non-Atomic Games, with R.J. Aumann, 1974.
  • "An Example of a Slow-Converging Core", 1975, IER.
  • "Cardinal Utility from Intensity Comparison", 1975, RAND.
  • "Solution Notions for Continuingly Competitive Situations", with R.J. Aumann, 1976.
  • "Competitive Outcomes in the Cores of Market Games" with M. Shubik, 1976, IJGT
  • "Noncooperative Generlal Exchange", 1976, in Lin, editor, Theory and Measurement of Economic Externalities.
  • "Trade Using One Commodity as a Means of Payment" with M.Shubik, 1977, JPE.
  • "An Example of a Trading Economy with Three Competitive Equilibria", 1977, with M.Shubik,, JPE
  • "Geometric Properties of the Kernel, Nucleolus and Related Solution Concepts", with B. Peleg and M. Maschler, 1979, Mathematics of Operations Research
  • "Convergence of the Bargaining Set for Differentiable Market Games", 1984, appendix in Shubik, A Game-Theoretic Approach to Political Economy.
  • "Long-Term Competition: A game-theoretic analysis", with R.J. Aumann, 1994, in Gale et al, editors, Essays in Game Theory
  • "Allocation Games: the deferred acceptance algorithm", 2012 [nobel]

 
HET

 
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Resources on L.S. Shapley

  • Lloyd S. Shapley's homepage at UCLA, including vita and bibliography
  • Shapley's faculty page at UCLA
  • 2012 Nobel Memorial Prize website: facts, biography, lecture
  • "Introduction to the Shapley Value", by Alvin E. Roth, 1988, The Shapley Value [pdf] [full pdf]
  • "Lloyd Shapley's Matching and Game Theory" by Roberto Serrano, 2012 [pdf]
  • "Shapley and Roth Awarded Nobel Prizes in Economics", 2012, AMS [pdf]
  • "Alvin E. Roth and Lloyd S. Shapley, Nobel Prizes in Economics 2012 for the Theory of Stable Allocations and the Practice of Market Design" by Jordi Masso, 2013 [pdf]
  • "Announcement of Nobel" article in NY Times, 2012
  • Shapley article at EJW [pdf]
  • Shapley bio at AEA
  • Citation from 1981 John von Neumann Theory Prize from INFORMS
  • Shapley page at repec/ideas
  • Shapley entry at Britannica
  • Wikipedia

 

 
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