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

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 cooperatie game theory focuses for the most part on the special case of games with transferable utilii v, 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 cotlcepts are inadequate either because they are undefined or they fail to exist, and even if they do exist, theyfocus 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 thit 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 definitio~i and motivation, nontrivial coalition predictions are made in conjunction with its payoff pt edictions. The Comb ptitive Solution's definition is entirely general, but a special class of gamesmajority ru: Kspatial games-are usedfor illustrations and the experimental test reported here consists of .ight plays of a 5-person spatial game that does not possess a main-simple Vsolution or i bargaining set. Overall, the data conform closely to the Competitive Solution's predictions.