International Journal of Game Theory

, Volume 2, Issue 1, pp 253–261 | Cite as

A characterization of polyhedral market games

  • L. J. Billera
  • R. E. Bixby
Papers

Abstract

The class of games without side payments obtainable from markets having finitely many commodities and continuous concave utility functions is considered. It is first shown that each of these so-called market games is totally balanced, for a reasonable generalization of the idea of a balanced side payment game. It is then shown that among polyhedral games (i.e., games for which each (V(S) is a polyhedron), this property characterizes the market games.

Keywords

Utility Function Economic Theory Game Theory Side Payment Market Game 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Billera, L. J.: Some theorems on the core of ann-person game without side payments. Siam J. Appl. Math.18, 567–579, 1970.Google Scholar
  2. —: A note on a kernel and the core for games without side payments. Technical Report No. 152, Dept. of O. R., Cornell U., June 1972.Google Scholar
  3. —: On games without side payments arising from a general class of markets. Technical Report No. 184, Dept. of O. R., Cornell U., June 1973.Google Scholar
  4. — and R. E.Bixby: A characterization of Pareto surfaces. Technical Report No. 162, Dept. of O. R., Cornell U., December 1972, (to appear in Proc. Amer. Math. Soc.).Google Scholar
  5. Scarf, H.: The core of ann-person game. Econometrica35, 50–69, 1967.Google Scholar
  6. Shapley, L. S.: On balanced games without side payments. Mathematical Programming, T. C. Hu and S. M. Robinson, Editors, Academic Press, New York, 1973.Google Scholar
  7. —, andM. Shubik: On market games. Journal of Economic Theory1, 9–25, 1969.Google Scholar

Copyright information

© Physica-Verlag Rudolf Liebing KG 1973

Authors and Affiliations

  • L. J. Billera
    • 1
  • R. E. Bixby
    • 2
  1. 1.Department of Operations ResearchCornell UniversityIthaca
  2. 2.Department of MathematicsUniversity of KentuckyLexington

Personalised recommendations