Collaboration Network Formation and the Demand for Problem Solvers with Heterogenous Skills

Collaborative problem solving is important in a wide range of contexts, including economic production, product development, academic research, and policy making. Here, I present a formal model of collaborative problem solving, in which individuals with heterogeneous skill sets collaborate to solve problems. I show that the number of problems an individual solves is a supermodular function of her set of skills, and cannot be determined by pricing her skills individually. I then look at the network formed by the collaborative links between problem solvers. An individual’s position in this network reflects the demand for her skills as a problem solver, and the overall structure of the network reflects the nature of the problem-solving community. I show that the degree distribution of the network will be fat-tailed–that is, a small number of players solve the vast majority of the problems, while most players solve relatively few. This result holds, even when skills are distributed independently across the problem solvers (Bernoulli Skills Model). The degree distribution becomes more skewed when problems are difficult for the population, and when skills are arranged into disciplines (the Ladder Model).