Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Cooperative Games

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_98-2

Glossary

Characteristic or coalitional function

The most usual way to represent a cooperative game.

Cooperative game

Strategic situation involving coalitions, whose formation assumes the existence of binding agreements among players.

Core

Solution concept that assigns the set of payoffs that cannot be improved upon by any coalition.

Game theory

Discipline that studies strategic situations.

Shapley value

Solution concept that assigns the average of marginal contributions to coalitions.

Solution concept

Mapping that assigns predictions to each game.

Definition of the Subject

Cooperative

It is one of the two counterparts of game theory. It studies the interactions among coalitions of game theory players. Its main question is this: Given the sets of feasible payoffs for each coalition, what payoff will be awarded to each player? One can take a positive or normative approach to answering this question, and different solution concepts in the theory lean towards one or the other.

Core

It is a...

Keywords

Cooperative Game Solution Concept Competitive Equilibrium Marginal Contribution Grand Coalition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Bibliography

Primary Literature

  1. Anderson RM (1978) An elementary core equivalence theorem. Econometrica 46:1483–1487MathSciNetCrossRefMATHGoogle Scholar
  2. Anderson RM (2008) Core convergence. In: Durlauff S, Blume L (eds) The new Palgrave dictionary of economics, 2nd edn. McMillan, LondonGoogle Scholar
  3. Aumann RJ (1964) Markets with a continuum of traders. Econometrica 32:39–50MathSciNetCrossRefMATHGoogle Scholar
  4. Aumann RJ (1975) Values of markets with a continuum of traders. Econometrica 43:611–646MathSciNetCrossRefMATHGoogle Scholar
  5. Aumann RJ (1985) An axiomatization of the non-transferable utility value. Econometrica 53:599–612MathSciNetCrossRefMATHGoogle Scholar
  6. Aumann RJ (1987) Game theory. In: Eatwell J, Milgate M, Newman P (eds) The new Palgrave dictionary of economics. Norton, New YorkGoogle Scholar
  7. Aumann RJ, Peleg B (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bull Am Math Soc 66:173–179CrossRefMATHGoogle Scholar
  8. Aumann RJ, Shapley LS (1974) Values of non-atomic games. Princeton University Press, PrincetonMATHGoogle Scholar
  9. Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games (in Russian). Problemy Kibernetiki 10(119):139MATHGoogle Scholar
  10. de Clppel G, Peters H, Zank H (2004) Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games. I J Game Theory 33:145–158MathSciNetCrossRefMATHGoogle Scholar
  11. Debreu G, Scarf H (1963) A limit theorem on the core of an economy. Int Econ Rev 4:235–246CrossRefMATHGoogle Scholar
  12. Deng X, Papadimitriou CH (1994) On the complexity of cooperative solution concepts. Math Oper Res 19:257–266MathSciNetCrossRefMATHGoogle Scholar
  13. Edgeworth FY (1881) Mathematical Psychics. Kegan Paul Publishers, London. (reprinted in 2003) Newman P (ed) F. Y. Edgeworths Mathematical Psychics and Further Papers on Political Economy. Oxford University Press, OxfordMATHGoogle Scholar
  14. Gillies DB (1959) Solutions to general non-zero-sum games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV. Princeton University Press, Princeton, pp 47–85Google Scholar
  15. Gul F (1989) Bargaining foundations of Shapley value. Econometrica 57:81–95MathSciNetCrossRefMATHGoogle Scholar
  16. Harsanyi JC (1963) A simplified bargaining model for the n-person cooperative game. Int Econ Rev 4:194–220CrossRefMATHGoogle Scholar
  17. Hart S (1985) An axiomatization of Harsanyi s non-transferable utility solution. Econometrica 53:1295–1314MathSciNetCrossRefMATHGoogle Scholar
  18. Hart S (2008) Shapley value. In: Durlauff S, Blume L (eds) The new Palgrave dictionary of economics, 2nd edn. McMillan, LondonGoogle Scholar
  19. Hart S, Mas-Colell A (1989) Potencial, value and consistency. Econometrica 57:589–614MathSciNetCrossRefMATHGoogle Scholar
  20. Hart S, Mas-Colell A (1996) Bargaining and value. Econometrica 64:357–380MathSciNetCrossRefMATHGoogle Scholar
  21. Krishna V, Serrano R (1995) Perfect equilibria of a model of n-person non-cooperative bargaining. I J Game Theory 24:259–272CrossRefMATHGoogle Scholar
  22. Mas-Colell A (1988) Algunos comentarios sobre la teoria cooperativa de los juegos. Cuadernos Economicos 40:143–161Google Scholar
  23. Maschler M, Owen G (1992) The consistent Shapley value for games without side payments. In: Selten R (ed) Rational interaction: essays in honor of John Harsanyi Springer, New YorkGoogle Scholar
  24. Moldovanu B, Winter E (1995) Order independent equilibria. Games Econ Behav 9:21–34MathSciNetCrossRefMATHGoogle Scholar
  25. Nash JF (1953) Two person cooperative games. Econometrica 21:128–140MathSciNetCrossRefMATHGoogle Scholar
  26. Peleg B (1985) An axiomatization of the core of cooperative games without side payments. J Math Econ 14:203–214ADSMathSciNetCrossRefMATHGoogle Scholar
  27. Peleg B (1986) On the reduced game property and its converse. I J Game Theory 15:187–200MathSciNetCrossRefMATHGoogle Scholar
  28. Pérez-Castrillo D (1994) Cooperative outcomes through non-cooperative games. Games Econ Behav 7:428–440CrossRefMATHGoogle Scholar
  29. Pérez-Castrillo D, Wettstein D (2001) Bidding for the surplus: a non-cooperative approach to the Shapley value. J Econ Theory 100:274–294MathSciNetCrossRefMATHGoogle Scholar
  30. Perry M, Reny P (1994) A non-cooperative view of coalition formation and the core. Econometrica 62:795–817MathSciNetCrossRefMATHGoogle Scholar
  31. Roth AE (2002) The economist as engineer: game theory, experimentation and computation as tools for design economics. Econometrica 70:1341–1378CrossRefMATHGoogle Scholar
  32. Scarf H (1967) The core of an N person game. Econometrica 38:50–69MathSciNetCrossRefMATHGoogle Scholar
  33. Serrano R (1995) A market to implement the core. J Econ Theory 67:285–294CrossRefMATHGoogle Scholar
  34. Serrano R (2005) Fifty years of the Nash program, 1953–2003. Investigaciones Económicas 29:219–258Google Scholar
  35. Serrano R, Vohra R (1997) Non-cooperative implementation of the core. Soc Choice Welf 14:513–525MathSciNetCrossRefMATHGoogle Scholar
  36. Serrano R, Volij O (1998) Axiomatizations of neoclassical concepts for economies. J Math Econ 30:87–108MathSciNetCrossRefMATHGoogle Scholar
  37. Shapley LS (1953) A value for n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317Google Scholar
  38. Shapley LS (1964) Values of large games VII: a general exchange economy with money. Research Memorandum 4248-PR RAND Corporation, Santa MonicaGoogle Scholar
  39. Shapley LS (1967) On balanced sets and cores. Nav Res Logist Q 14:453–460CrossRefGoogle Scholar
  40. Shapley LS (1969) Utility comparison and the theory of games. In: La Décision: Agrégation et Dynamique des Ordres de Préférence. CNRS, ParisGoogle Scholar
  41. Shapley LS (1971) Cores of convex games. I J Game Theory 1:11–26MathSciNetCrossRefMATHGoogle Scholar
  42. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonMATHGoogle Scholar
  43. Walras L (1874) Elements of pure economics, or the theory of social wealth. English edition: Jaffé W (ed) Reprinted in 1984 by Orion Editions, PhiladelphiaGoogle Scholar
  44. Winter E (1994) The demand commitment bargaining and snowballing of cooperation. Econ Theory 4:255–273Google Scholar
  45. Young HP (1985) Monotonic solutions of cooperative games. I J Game Theory 14:65–72MathSciNetCrossRefMATHGoogle Scholar

Books and Reviews

  1. Myerson RB (1991) Game theory: an analysis of conflict. Harvard University Press, CambridgeMATHGoogle Scholar
  2. Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, CambridgeMATHGoogle Scholar
  3. Peleg B, Sudholter P (2003) Introduction to the theory of cooperative games, 2nd edn. Kluwer/Springer, Amsterdam/BerlinGoogle Scholar
  4. Roth AE, Sotomayor M (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of EconomicsBrown UniversityProvidenceUSA