A Study of Skills, Problem Solving, and Collaboration Networks.

Abstract

Problem solving plays an important role in many contexts, including scientific innovation and economic production. Individual problem solvers work together, combining their skills to innovate and solve problems that none of them could solve alone. The collaborative links between individuals form a network, the structure of which affects behavior and outcomes. This thesis focuses on the formation of collaboration networks, specialization in problem solving populations, and the effect of network structure on group formation.

In the first chapter, I present a formal model of collaborative problem solving. I show that the number of collaborators an individual has is a highly non-linear function of her set of skills. I show that the degree distribution of the network as a whole 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. The degree distribution becomes more skewed when problems are difficult for the population, and when skills are arranged into disciplines.

In the second chapter, I examine the equilibrium population of specialists and generalists in problem solving communities. I show that if problems are one-dimensional, a population of generalists can only be sustained if there are significant barriers between disciplines. I then evaluate the social optimality of this equilibrium. I find that because generalists internalize the costs of diversifying their skills, some populations suffer from an undersupply of generalists, suggesting that more problems may be solved by subsidizing the costs of skill diversification.

In the final chapter, I model how individuals form problem solving teams when constrained by an exogenous social network. I show that without network constraints, the equilibrium of a sequential group formation game is highly suboptimal--groups tend to be much too large. I then introduce an exogenous social network constraint, and show that this constraint mitigates the tendency for groups to get too large. The efficiency of the equilibrium depends on the topology of the underlying social network; as the social network becomes more sparse, social welfare increases.