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Social network and private provision of public goods

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Abstract

Using a simple model with interdependent utilities, we study how social networks influence individual voluntary contributions to the provision of a public good. Departing from the standard model of public good provision, we assume that an agent’s utility has two terms: (a) ‘ego’-utility derived from the agent’s consumption of public and private goods, and (b) a social utility which is the sum of utility spillovers from other agents with whom the agent has social relationships. We establish conditions for the existence of a unique interior Nash equilibrium and describe the equilibrium in terms of network characteristics. We show that social network always has a positive effect on the provision of the public good. We also find that, in networks with “small world”-like modular structures, ‘bridging’ ties connecting distant parts of social network play an important role inducing an agent’s contribution to public good. Assumptions and results of the model are discussed in relation to the role of social capital in community-level development projects and to the effect of innovation networks on firms’ R&D investments.

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Notes

  1. Bonacich centrality is a measure used in social network analysis to describe the power and importance of an actor in a social network.

  2. Examples of such systems include systems of utilities in which individuals care equally for all other individuals and systems with a fixed pattern of interactions. For instance, Bergstrom (1999) examines a model where agents are located on a line and each agent is connected to exactly one agent on the right and one agent on the left. (This system of utility functions can be used in the framework of overlapping generations to account for intergenerational altruism.)

  3. Also see Bergstrom (2006).

  4. Ley (1997) has shown, that in a system of interrelated utilities such as (2), Pareto efficiency of an allocation is independent of the distribution of private consumption. However, this result concerns only the flat part of the utility possibility frontiers, because his analysis excludes corner solutions.

  5. Matrices of form (I−A) and their inverse are well-known to economists in the context of input-output analysis. Matrix B=(I−A)−1, where A is a matrix of technical coefficients, is a Leontief inverse that describes the relationship between vector of sector outputs and final demands. When a network defined by adjacency matrix A is strongly connected, a diagonally dominant matrix (I−A) is an M-matrix (Horn and Johnson 1994, p.131)

  6. The general version of their model with heterogeneous payoff impacts and upper bound on agents’ actions (Bramoullé et al. 2014, p.919).

  7. By assumption, the marginal rate of transformation between private and public goods is equal to 1.

  8. The Samuelson condition for the egoistic society would result in the same expression for \(\hat {Y}\).

  9. In social networks, those clusters may correspond to members of the same family, same neighborhood, close circles of colleagues, or same leader’s constituency, etc. For example, Arora and Sanditov (2015) studied social networks of farmers in a village in Southern India and found that clusters of farmers in this network are formed around cluster leaders, most of whom are important persons in the village.

  10. The lower the value of α, the shorter the effective distance across which utility spillovers flow and, consequently, the lower the importance of agent A bridging the three clusters.

  11. The value of α must be lower than 1/(2k+1) for matrix (I−A) to be dominant diagonal.

  12. From the population of random small-world networks, we sample only networks satisfying two sets of conditions: they produce dominant diagonal matrices (I−A) and they meet the conditions of Proposition 1. With larger values of α, Monte-Carlo simulations become impractical because most randomly generated networks fail those conditions.

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Acknowledgments

We are grateful to two anonymous referees and the guest editor, Zakaria Babutsidze, for valuable comments. Previous versions have benefitted from generous input provided by Francesco Lissoni, Uwe Cantner, Mauro Napoletano and the participants of EMAEE’13, WEHIA’13, GCW’13 conferences, the GREThA seminar at University of Bordeaux and Jena Economic Research Seminar at Friedrich Schiller University. The usual disclaimer applies.

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  1. TELECOM Ecole de Management, Institut Mines-Télécom, 9 rue Charles Fourier, 91011, Evry Cedex, France

    Bulat Sanditov

  2. Science Policy Research Unit, University of Sussex, Brighton, UK

    Saurabh Arora

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  1. Bulat Sanditov
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  2. Saurabh Arora
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Correspondence to Bulat Sanditov.

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Sanditov, B., Arora, S. Social network and private provision of public goods. J Evol Econ 26, 195–218 (2016). https://doi.org/10.1007/s00191-015-0436-2

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