Skip to main content

Cooperative Games

  • Reference work entry
  • First Online:
Complex Social and Behavioral Systems

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer Science+Business Media LLC 2017

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.

...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 379.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

Primary Literature

  • Anderson RM (1978) An elementary core equivalence theorem. Econometrica 46:1483–1487

    MathSciNet  MATH  Google Scholar 

  • Anderson RM (2008) Core convergence. In: Durlauff S, Blume L (eds) The new Palgrave dictionary of economics, 2nd edn. McMillan, London

    Google Scholar 

  • Aumann RJ (1964) Markets with a continuum of traders. Econometrica 32:39–50

    MathSciNet  MATH  Google Scholar 

  • Aumann RJ (1975) Values of markets with a continuum of traders. Econometrica 43:611–646

    MathSciNet  MATH  Google Scholar 

  • Aumann RJ (1985) An axiomatization of the non-transferable utility value. Econometrica 53:599–612

    MathSciNet  MATH  Google Scholar 

  • Aumann RJ (1987) Game theory. In: Eatwell J, Milgate M, Newman P (eds) The new Palgrave dictionary of economics. Norton, New York

    Google Scholar 

  • Aumann RJ, Peleg B (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bull Am Math Soc 66:173–179

    MATH  Google Scholar 

  • Aumann RJ, Shapley LS (1974) Values of non-atomic games. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games (in Russian). Problemy Kibernetiki 10(119):139

    MATH  Google Scholar 

  • 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 33:145–158

    MathSciNet  MATH  Google Scholar 

  • Debreu G, Scarf H (1963) A limit theorem on the core of an economy. Int Econ Rev 4:235–246

    MATH  Google Scholar 

  • Deng X, Papadimitriou CH (1994) On the complexity of cooperative solution concepts. Math Oper Res 19:257–266

    MathSciNet  MATH  Google Scholar 

  • 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, Oxford

    Google Scholar 

  • 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 47–85

    MATH  Google Scholar 

  • Gul F (1989) Bargaining foundations of Shapley value. Econometrica 57:81–95

    MathSciNet  MATH  Google Scholar 

  • Harsanyi JC (1963) A simplified bargaining model for the n-person cooperative game. Int Econ Rev 4:194–220

    MATH  Google Scholar 

  • Hart S (1985) An axiomatization of Harsanyi s non-transferable utility solution. Econometrica 53:1295–1314

    MathSciNet  MATH  Google Scholar 

  • Hart S (2008) Shapley value. In: Durlauff S, Blume L (eds) The new Palgrave dictionary of economics, 2nd edn. McMillan, London

    Google Scholar 

  • Hart S, Mas-Colell A (1989) Potencial, value and consistency. Econometrica 57:589–614

    MathSciNet  MATH  Google Scholar 

  • Hart S, Mas-Colell A (1996) Bargaining and value. Econometrica 64:357–380

    MathSciNet  MATH  Google Scholar 

  • Krishna V, Serrano R (1995) Perfect equilibria of a model of n-person non-cooperative bargaining. I J Game Theory 24:259–272

    MATH  Google Scholar 

  • Mas-Colell A (1988) Algunos comentarios sobre la teoria cooperativa de los juegos. Cuadernos Economicos 40:143–161

    Google Scholar 

  • 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 York

    Google Scholar 

  • Moldovanu B, Winter E (1995) Order independent equilibria. Games Econ Behav 9:21–34

    MathSciNet  MATH  Google Scholar 

  • Nash JF (1953) Two person cooperative games. Econometrica 21:128–140

    MathSciNet  MATH  Google Scholar 

  • Peleg B (1985) An axiomatization of the core of cooperative games without side payments. J Math Econ 14:203–214

    MathSciNet  MATH  Google Scholar 

  • Peleg B (1986) On the reduced game property and its converse. I J Game Theory 15:187–200

    MathSciNet  MATH  Google Scholar 

  • Pérez-Castrillo D (1994) Cooperative outcomes through non-cooperative games. Games Econ Behav 7:428–440

    MATH  Google Scholar 

  • Pérez-Castrillo D, Wettstein D (2001) Bidding for the surplus: a non-cooperative approach to the Shapley value. J Econ Theory 100:274–294

    MathSciNet  MATH  Google Scholar 

  • Perry M, Reny P (1994) A non-cooperative view of coalition formation and the core. Econometrica 62:795–817

    MathSciNet  MATH  Google Scholar 

  • Roth AE (2002) The economist as engineer: game theory, experimentation and computation as tools for design economics. Econometrica 70:1341–1378

    MATH  Google Scholar 

  • Scarf H (1967) The core of an N person game. Econometrica 38:50–69

    MathSciNet  MATH  Google Scholar 

  • Serrano R (1995) A market to implement the core. J Econ Theory 67:285–294

    MATH  Google Scholar 

  • Serrano R (2005) Fifty years of the Nash program, 1953–2003. Investigaciones Económicas 29:219–258

    Google Scholar 

  • Serrano R, Vohra R (1997) Non-cooperative implementation of the core. Soc Choice Welf 14:513–525

    MathSciNet  MATH  Google Scholar 

  • Serrano R, Volij O (1998) Axiomatizations of neoclassical concepts for economies. J Math Econ 30:87–108

    MathSciNet  MATH  Google Scholar 

  • 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 307–317

    Google Scholar 

  • Shapley LS (1964) Values of large games VII: a general exchange economy with money. Research Memorandum 4248-PR RAND Corporation, Santa Monica

    Google Scholar 

  • Shapley LS (1967) On balanced sets and cores. Nav Res Logist Q 14:453–460

    Google Scholar 

  • Shapley LS (1969) Utility comparison and the theory of games. In: La Décision: Agrégation et Dynamique des Ordres de Préférence. CNRS, Paris

    Google Scholar 

  • Shapley LS (1971) Cores of convex games. I J Game Theory 1:11–26

    MathSciNet  MATH  Google Scholar 

  • von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Walras L (1874) Elements of pure economics, or the theory of social wealth. English edition: Jaffé W (ed) Reprinted in 1984 by Orion Editions, Philadelphia

    Google Scholar 

  • Winter E (1994) The demand commitment bargaining and snowballing of cooperation. Econ Theory 4:255–273

    Google Scholar 

  • Young HP (1985) Monotonic solutions of cooperative games. I J Game Theory 14:65–72

    MathSciNet  MATH  Google Scholar 

Books and Reviews

  • Myerson RB (1991) Game theory: an analysis of conflict. Harvard University Press, Cambridge

    MATH  Google Scholar 

  • Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, Cambridge

    MATH  Google Scholar 

  • Peleg B, Sudholter P (2003) Introduction to the theory of cooperative games, 2nd edn. Kluwer/Springer, Amsterdam/Berlin

    Google Scholar 

  • Roth AE, Sotomayor M (1990) Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roberto Serrano .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Serrano, R. (2020). Cooperative Games. In: Sotomayor, M., Pérez-Castrillo, D., Castiglione, F. (eds) Complex Social and Behavioral Systems . Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0368-0_98

Download citation

Publish with us

Policies and ethics