Public Choice

, Volume 22, Issue 1, pp 91–102 | Cite as

Inessential games and non-imposed solutions to allocation problems

  • Charles Bird


The basic objective of this paper has been to develop some mathematical models for shortage situations (both real and psychological) in which the solution is determined by the participants. The purpose of these models is to highlight some of the inequities which may result when such bargaining goes on and to observe that under certain conditions the structure of the game is such that each player may be able to salvage at least a partial allocation. This can occur when the game is not status quo stable for power weighted solutions, or when priorities are equal for priority solutions. Majority solutions can counteract powerful groups and can minimize the number of unsatiated parties. But some majority solutions can also be unfair by discriminating against the remaining players. These models may be of some use in determining whether or not outside regulation of a particular situation is a sound policy.


Mathematical Model Public Finance Allocation Problem Basic Objective Powerful Group 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aumann, R. J. and M. Maschler, “The Bargaining Set for Cooperative Games”, inAdvances in Game Theory, Eds. M. Dresher, L. S. Shapley, and A. W. Tucker, Annals of Mathematics Studies52, Princeton University Press, Princeton, N.J., 1964, 443–476.Google Scholar
  2. [2]
    Bird, C., “Extension of Bargaining Concepts to Infinite Player Games”, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, Pa., 1973.Google Scholar
  3. [3]
    Bird, C. and K. O. Kortanek, “Game Theoretic Approaches to Some Air Pollution Regulation Problems”. Socio-Economic Planning Sciences, to appear.Google Scholar
  4. [4]
    Chanes, A. and K. O. Kortanek, “On Classes of Convex Preemptive Nuclei for n-person Games”,Proceedings of the Princeton Symposium on Mathematical Programming, edited by H. Kuhn, Princeton University Press, 1970, 377–390.Google Scholar
  5. [5]
    Heany, James P. “Mathematical Programming Model for Long Range River Basin Planning with Emphasis on the Colorado River Basin”, Ph.D. Thesis, Northwestern University, Evanston, Illinois, 1968.Google Scholar
  6. [6]
    Littlechild, S. C., “A Game Theoretic Approach to Public Utility Pricing,”Western Economic Journal, v. 8, No. 2 (1970), 162–166.Google Scholar
  7. [7]
    Sorenson, S., “A Mathematical Theory of Coalitions and Competition in Resource Development”, Ph. D. Thesis, University of Texas at Austin, April 1972.Google Scholar

Copyright information

© Center for Study of Public Choice Virginia Polytechnic Institute and State University 1974

Authors and Affiliations

  • Charles Bird
    • 1
  1. 1.Department of Pure and Applied Math.Washington State UniversityUSA

Personalised recommendations