The Competitive Solution for <i>N</i>-Person Games Without Transferable Utility, With an Application to Committee Games

TLDR

Cooperative game theory largely assumes transferable utility, limiting its ability to model many political coalition processes, and standard solution concepts are often undefined or fail to predict likely coalitions in the general case. The paper introduces and experimentally tests the Competitive Solution, a new concept for n‑person cooperative games that addresses the shortcomings of existing solution concepts. The Competitive Solution is defined generally and illustrated by applying it to majority‑rule spatial games, with an experimental test comprising eight plays of a 5‑person spatial game that lacks a main‑simple V‑solution or bargaining set. Experimental data from the eight plays closely match the Competitive Solution’s predictions.

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.