Tim Hellmann

Evolution of Social Networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.

On the existence and uniqueness of pairwise stable networks

In this paper we show how externalities between links affect the existence and uniqueness of pairwise stable (PS) networks. For this we introduce the properties ordinal convexity (concavity) and ordinal strategic complements (substitutes) of utility functions on networks. It is shown that there exists at least one PS network if the profile of utility functions is ordinal convex and satisfies the ordinal strategic complements property. On the other hand, ordinal concavity and ordinal strategic substitutes are sufficient for some uniqueness properties of PS networks. Additionally, we elaborate on the relation of the link externality properties to definitions in the literature.

The Evolution of R&D Networks

We study the evolution of R&D networks in a Cournot model where firms may lower marginal costs due to bilateral R&D collaborations. Stochastically stable R&D networks exhibit the dominant group architecture, and, contrary to the existing literature, generically unique predictions about the size of the dominant group can be obtained. This size decreases monotonically with respect to the cost of link formation and there exists a lower bound on the size of the dominant group for non-empty networks. Stochastically stable networks are always inefficient and an increase in linking costs has a non-monotone effect on average industry profits.

Strategic Formation of Homogeneous Bargaining Networks

We analyze a model of strategic network formation prior to a Manea (2011) bargaining game: ex-ante homogeneous players form costly undirected links anticipating expected equilibrium payoffs from the subsequent network bargaining. Assuming patient players, we provide a complete characterization of non-singularly pairwise (Nash) stable networks: specific disjoint unions of separated pairs, odd circles and isolated players constitute this class. We also show that many generic structures are not even singularly pairwise stable. As an important implication, this reveals the diversity of possible bargaining outcomes to be substantially narrowed down provided pairwise stability. Further, for sufficiently high costs the pairwise stable and efficient networks coincide whereas this does not hold if costs are low or at an intermediate level. As a robustness check, we also study the case of time-discounting players.

R&D Investments Under Endogenous Cluster Formation

We study investments in R&D and the formation of R&D clusters of firms which are competitors in the market. Firms first decide on long-term R&D investment, then form research clusters according to the unanimity game, and finally compete in quantities. Equilibria with no-investment might co-exist with equilibria where a large fraction of firms invest in R&D. Firms tend to over-invest compared to a scenario where research clusters are ex-ante fixed and also compared to the welfare optimum.