The Economics of Scientific Research Coalitions: Collaborative Network Formation in the Presence of Multiple Funding Agencies

Abstract

The paper develops a formal model of coalition-building (“network” formation) among research units that seek competitive funding from a supra-regional program, while also drawing support from their respective regional funding agencies. This approach enables one to ask whether there are stable (equilibrium) outcomes in the interactions among the several funding entities, and to investigate what those outcomes would imply for the evolving distribution of scientific performance within the entire region and its national sub-regions. This analysis is motivated by the absence of frameworks of analysis applicable to problems of design of public R&D funding arrangements in the European Union, and in other regional systems were independent programs of “federal and state” support for research co-exists First, a model is developed to analyze how collaborations are formed under different sets of funding rules of an international funding institution, starting with a fixed finite population of research units and an associated distribution of reputed quality, or scientific reputation.. Collaborations are formed in the expectation of attracting supra-national funding, following a specific ordering procedure; this gives rise to a repeated non-cooperative game of coalition (or collaboration) formation with the distribution of payoffs within the collaboration following to a fixed rule. Non- cooperative games of coalition formation developed by Bloch (1995), and Ray and Vohra (1999), provides a useful framework single-period framework. Following Keely (1999), this type of game is applied to a multi-period setting in which a distribution of coalitions is tracked, along with the levels of funding received. The latter are determined according to a rule comparing the distribution of reputations within and across collaborations. Alternative possible external funding rules are analyzed to determine how they impact upon collaboration formation, and the resulting evolution of the reputation distribution (as that will be affected by the allocation of funding). In the second part of the analysis, various combinations of national and supra-national funding regimes are examined, but all the rules considered stipulate that collaborations are funded as a whole, regardless of the number of members; and that their funding is determined by the absolute level of average reputation, or of the variance in reputation, rather than just the rankings of the proposed networks. The Nash equilibria associated with each of the stipulated funding regimes can be compared, and to characterize the outcomes, the paper examines these two moments of the endogenously determined distributions research “competence” (signaled by the reputation measures) within the entire ensemble of research units and its national partitions. A numerical simulation helps illustrate the nature of the conclusions for policy design that can be drawn from this style of analysis.