Skip to main content

Values of Large Market Games

  • Chapter
Applied Game Theory

Abstract

Three aspects of the application of the game theoretic concept of “value” to non-atomic economies — such as markets or production — are studied: first, the relation between value and equilibria; second, the problems of existence and non-existence of value; and third, a new way of defining value for these games, in order to guarantee its existence, which leads to interesting economic interpretations.

1) This work was supported by National Science Foundation Grant SOC75–21820 at the Institute for Mathematical Studies in the Social Sciences, Stanford University. Presented at the International Conference on Applied Game Theory, Vienna, June 1978.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arrow, K.J., and F.H.Hahn: General Competitive Analysis, San Francisco 1971.

    MATH  Google Scholar 

  • Aumann, R.J.: Markets with a Continuum of Traders. Econometrica 32, 1964, 39–50.

    Article  MATH  MathSciNet  Google Scholar 

  • Aumann, R.J.: Values of Markets with a Continuum of Traders. Econometrica 43, 1975, 611–646.

    Article  MATH  MathSciNet  Google Scholar 

  • Aumann, R.J., and M.Kurz: Power and Taxes in a Multi-Commodity Economy. Israel Journal of Mathematics 27, 1977, 185–234.

    Article  MATH  MathSciNet  Google Scholar 

  • Aumann, R.J., and M.Perles: A Variational Problem Arising in Economics. Journal of Mathematical Analysis and Applications 11, 1965, 488–503.

    Article  MATH  MathSciNet  Google Scholar 

  • Aumann, R.J., and L.S.Shapley: Values of Non-Atomic Games. Princeton 1974.

    MATH  Google Scholar 

  • Champsaur, P.: Cooperation Versus Competition. Journal of Economic Theory 11, 1975, 394–417.

    Article  MATH  MathSciNet  Google Scholar 

  • Debreu, G., and H.Scarf: A Limit Theorem on the Core of an Economy. International Economic Review 4, 1963, 235–246.

    Article  MATH  Google Scholar 

  • Harsanyi, J.: A Bargaining Model for the Cooperative «-Person Game. Annals of Mathematical Studies 40, 1959, 325–355.

    MATH  MathSciNet  Google Scholar 

  • Hart, S.: Asymptotic Value of Games with a Continuum of Players. Journal of Mathematical Economics 4, 1977a, 57–80.

    Article  MATH  MathSciNet  Google Scholar 

  • Hart, S.: Values of Non-Differentiable Markets with a Continuum of Traders. Journal of Mathematical Economics 4, 1977b, 103–116.

    Article  MATH  MathSciNet  Google Scholar 

  • Hart, S.: Measure-Based Values of Market Games. TR# 254, Economics Series. Institute for Mathematical Studies in the Social Sciences, Stanford University, 1978, forthcoming in Mathematics of Operations Research.

    Google Scholar 

  • Hildenbrand, W.: Core and Equilibria in a Large Economy. Princeton 1974.

    Google Scholar 

  • Kannai, Y.: Values of Games with a Continuum of Players. Israel Journal of Mathematics 4, 1966, 54–58.

    Article  MATH  MathSciNet  Google Scholar 

  • Mas-Colell, A.: Competitive and Value Allocations of Large Exchange Economies. Journal of Economic Theory 14, 1977,419–438.

    Article  MATH  MathSciNet  Google Scholar 

  • Rockafellar, R.T.: Convex Analysis. Princeton 1970.

    MATH  Google Scholar 

  • Shapley, L.S.: Values of Large Games VII: A General Exchange Economy with Money. RM-4248-PR, The Rand Corporation, Santa Monica, California, 1964.

    Google Scholar 

  • Shapley, L.S.: Utility Comparison and the Theory of Games. La Decision. Paris 1969.

    Google Scholar 

  • Vind, K.: Edgeworth Allocations in an Exchange Economy with Many Traders. International Economic Review 5, 1964, 165–177.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

S. J. Brams A. Schotter G. Schwödiauer

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hart, S. (1979). Values of Large Market Games. In: Brams, S.J., Schotter, A., Schwödiauer, G. (eds) Applied Game Theory. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-41501-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-41501-6_11

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0208-5

  • Online ISBN: 978-3-662-41501-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics