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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
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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

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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.

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