Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2025-01-04T23:27:25.375Z Has data issue: false hasContentIssue false
  • English
  • Français

The Competitive Solution for N-Person Games Without Transferable Utility, With an Application to Committee Games*

Published online by Cambridge University Press:  01 August 2014

Richard D. McKelvey ,
Peter C. Ordeshook  and
Mark D. Winer
Richard D. McKelvey
Affiliation:
Carnegie-Mellon University
Peter C. Ordeshook
Affiliation:
Carnegie-Mellon University
Mark D. Winer
Affiliation:
Carnegie-Mellon University
Get access Rights & Permissions [Opens in a new window]

Abstract

This essay defines and experimentally tests a new solution concept for n-person cooperative games—the Competitive Solution. The need for a new solution concept derives from the fact that cooperative game theory focuses for the most part on the special case of games with transferable utility, even though, as we argue here, this assumption excludes the possibility of modelling most interesting political coalition processes. For the more general case, though, standard solution concepts are inadequate either because they are undefined or they fail to exist, and even if they do exist, they focus on predicting payoffs rather than the coalitions that are likely to form.

The Competitive Solution seeks to avoid these problems, but it is not unrelated to existent theory in that we can establish some relationships (see Theorems 1 and 2) between its payoff predictions and those of the core, the V-solution and the bargaining set. Additionally, owing to its definition and motivation, nontrivial coalition predictions are made in conjunction with its payoff predictions.

The Competitive Solution's definition is entirely general, but a special class of games—majority rule spatial games—are used for illustrations and the experimental test reported here consists of eight plays of a 5-person spatial game that does not possess a main-simple V-solution or a bargaining set. Overall, the data conform closely to the Competitive Solution's predictions.

Type
Research Article
Information
American Political Science Review , Volume 72 , Issue 2 , June 1978 , pp. 599 - 615
Copyright
Copyright © American Political Science Association 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The authors would like to thank the National Science Foundation for its support of this research. We also thank James D. Laing for his many helpful suggestions in preparing this paper and in the conduct of our experimental research, and Phillip Straffin for his perceptive comments.

References

Aumann, Robert J. (1967). “A Survey of Cooperative Games Without Side Payments.” In Shubik, M. (ed.), Essays in Mathematical Economics in Honor of Oskar Morgenstern. Princeton: Princeton University Press.Google Scholar
Aumann, Robert J., and Maschler, M. (1964). “The Bargaining Set for Cooperative Games.” In Dresher, M., Shapley, L. S. and Tucker, A. W. (eds.), Advances in Game Theory. Annals of Mathematical Studies, No. 52, Princeton: Princeton University Press.Google Scholar
Berl, J., McKelvey, R., Ordeshook, P. C., and Winer, M. (1976). “An Experimental Test of the Core in a Simple N-Person Cooperative Non Sidepayment Game.” Journal of Conflict Resolution 20:453–79.CrossRefGoogle Scholar
Butterworth, Robert (1971). “A Research Note on the Size of Winning Coalitions.” American Political Science Review 65:741–48.CrossRefGoogle Scholar
deSwaan, Abraham (1973). Coalition Theories and Cabinet Formation. San Francisco: Jossey Bass.Google Scholar
Downs, Anthony (1957). An Economic Theory of Democracy. New York: Harper and Row.Google Scholar
Fiorina, Morris, and Plott, Charles (1978). “Committee Decisions Under Majority Rule: An Experimental Study,” American Political Science Review 72:575–98.CrossRefGoogle Scholar
Frohlich, Norman (1975). “The Instability of Minimum Winning Coalitions.” American Political Science Review 69:943–46.CrossRefGoogle Scholar
Horowitz, Abraham D., and Rapoport, Amnon (1974). “Test of the Kernel and Two Bargaining Set Models in Four- and Five-person Games.” In Rapoport, Anatol (ed.), Game Theory as a Theory of Conflict Resolution. Boston: Reidel Publishing Company.Google Scholar
Kahn, J. P., and Rapoport, Amnon (1972). “Test of the Bargaining Set and Kernel Model in Three-Person Games.” Report No. 112, Thurston Psychometric Laboratory, University of North Carolina, pp. 161–92.Google Scholar
Laing, J. D., and Morrison, Richard J. (1974). “Sequential Games of Status.” Behavioral Science 19:177–196.CrossRefGoogle Scholar
McKelvey, R. D., and Smith, R. (1975). “Internal Stability and the Size Principle.” Mimeographed, Carnegie-Mellon University.Google Scholar
McKelvey, R. D., and Ordeshook, P. C. (1976). “Symmetric Spatial Games Without Majority Rule Equilibria.” American Political Science Review 70:1172–84.CrossRefGoogle Scholar
McKelvey, R. D., and Ordeshook, P. C. (1978). “Competitive Coalition Theory.” In Ordeshook, P. C. (ed.), Game Theory and Political Science. New York: New York University Press.Google Scholar
Ordeshook, P. C. (1976). “Spatial Models of Election Competition: A Survey and Critique.” In Budge, and Crewe, (eds.), Party Identification and Beyond. New York: Wiley.Google Scholar
Peleg, B. (1963). “Bargaining Sets of Cooperative Games Without Sidepayments.” Israel Journal of Mathematics 1:197–200.CrossRefGoogle Scholar
Plott, Charles R. (1967). “A Notion of Equilibrium and Its Possibility Under Majority Rule.” American Economic Review 57: 787–806.Google Scholar
Riker, William H. (1967). “Bargaining in a Three-Person Game.” American Political Science Review 61:642–56.CrossRefGoogle Scholar
Riker, W. H., and Zavoina, W. J. (1970). “Rational Behavior in Politics: Evidence from a Three-Person Game.” American Political Science Review 64:48–60.CrossRefGoogle Scholar
Riker, W. H. (1962). The Theory of Political Coalitions. New Haven: Yale University Press.Google Scholar
Scarf, Herbert E. (1967). “On the Core of an N Person Game.” Econometrica 35, 1:50–69.CrossRefGoogle Scholar
Schofield, Norman (1976). “The Kernel and Payoffs in European Government Coalitions.” Public Choice 26:29–49.CrossRefGoogle Scholar
Shepsle, Kenneth (1974). “On the Size of Winning Coalitions.” American Political Science Review 68:505–18. (Comment and Rejoinder, 519–24.)CrossRefGoogle Scholar
Sloss, Judith (1973). “Stable Outcomes in Majority Voting Games.” Public Choice 15:19–48.CrossRefGoogle Scholar
Taylor, Michael (1972). “On the Theory of Government Coalition Formation.” British Journal of Political Science 2:361–73.CrossRefGoogle Scholar
Wilson, Robert (1971). “Stable Coalition Proposals in Majority-Rule Voting.” Journal of Economic Theory 3:254–71.CrossRefGoogle Scholar
Submit a response

Comments

No Comments have been published for this article.