A model of weighted network formation

Abstract

This paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either “reciprocal” or “nonreciprocal.” In a reciprocal equilibrium, any two agents invest equally in the link between them. In a nonreciprocal equilibrium, agents are partitioned into “concentrated” and “diversified” agents, and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and are not efficient due to the positive externalities of investing in a link.

Efficiency and Stability in a Process of Teams Formation

“…In particular, this is in line with the assumptions of the model in [1], where the benefit of an agent from participating to a project always increases if she gets involved in it. Moreover, this assumption is consistent with the behavior of researchers that we observe in the APS dataset discussed in Sect.…”

“…To refine this myopic equilibrium concept with stochastic stability we use the same approach of [24] while extending their model, which is a special case of the one presented here. Moreover, we contribute to this stream of literature by incorporating constraints to the capacity of agents of performing tasks and of coordinating with others in the spirit of [46] and [1], although both works consider a pure noncooperative framework in contrast with our approach which is more cooperative.…”

“…We consider the American Physical Society dataset (APS), which comprises publications spanning several decades in virtually all fields of physics and also contains information about their references and their authors. 1 This allows building a co-authorship network where a link between two authors is established if and only if they are both authors of a paper and, in addition, it allows the computation of the citations received by every paper (and, hence, by each author).…”

“…4.5). 1 The dataset consists of around 300,000 authors and 570,000 papers published from the beginning of the XX century until 2015. To avoid the scarcity of data before the 1950s, here we only focus on the most consistent part of this dataset, thus limiting our attention to papers published from 1960 and, consequently, to authors whose career started after 1960 as well.…”

Essays on the economics of social networks

“…In fact, B's decision to form a new link positively influences his neighbours' neighbour, while affecting his direct neighbours negatively. In its core idea of nodes differentiating the investment they commit to their neighbours this chapter is closest to Baumann (2021). She analyses a model of weighted network formation and characterises the types of equilibria that occur.…”