Skip to main content

Social network and private provision of public goods


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  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 (IA) and their inverse are well-known to economists in the context of input-output analysis. Matrix B=(IA)−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 (IA) 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 (IA) 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 (IA) 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.


  • Arora S, Sanditov B (2015) Cultures of caste and rural development in the social network of a South Indian Village. Sage Open 5(3)

  • Arrow K (1962) Economic welfare and the allocation of resources for invention. In: Nelson R.R. (ed) The rate and direction of inventive activity: economic and social factors. National Bureau of Economic Research, pp 609–626

  • Balland P-A (2012) Proximity and the evolution of collaboration networks: evidence from research and development projects within the global navigation satellite system (GNSS) industry. Regional Studies 46(6):741–756

    Article  Google Scholar 

  • Ballester C, Calvó-Armengol A, Zenou Y (2006) Who’s who in networks. wanted: the key player. Econometrica 74(5):1403–1417

    Article  Google Scholar 

  • Becker G (1976) A theory of social interactions. J Polit Econ 82:1063–1094

    Article  Google Scholar 

  • Bergstrom TC (1999) Systems of benevolent utility functions. J Public Econ Theory 1(1):71–100

    Article  Google Scholar 

  • Bergstrom TC (2006) Benefit-cost in a benevolent society. Am Econ Rev 96 (1):339–351

    Article  Google Scholar 

  • Bergstrom TC, Cornes RC (1983) Independence of allocative efficiency from distribution in the theory of public goods. Econometrica 51(6):1753–1765

    Article  Google Scholar 

  • Bloch F, Zenginobuz Ü (2007) The effect of spillovers on the provision of local public goods. Rev Econ Des 11(3):199–216

    Google Scholar 

  • Boschma R (2010) Proximity and innovation: a critical assessment. Reg. Stud. 39(1):61–74

    Article  Google Scholar 

  • Bourdieu P (1986) The forms of capital. In: Richardson J (ed) Handbook of theory and research for the sociology of education. Greenwood

  • Bourlès R, Bramoullé Y (2013) Altruism in networks. mimeo

  • Bramoullé Y, Kranton R (2007) Public goods in networks. J Econ Theory 135(1):478–494

    Article  Google Scholar 

  • Bramoullé Y, Kranton R, D’Amours M (2014) Strategic interaction and networks. Am Econ Rev 104(3):898–930

    Article  Google Scholar 

  • Burt R (2000) The network structure of social capital. Res Organ Behav 22:345–423

    Article  Google Scholar 

  • Cohen WM, Levinthal DA (1989) Innovation and learning: the two faces of R&D. Econ J 99(397):569–96

    Article  Google Scholar 

  • Cowan R, Jonard N (2003) The dynamics of collective invention. J Econ Behav Organ 52(4):513–532

    Article  Google Scholar 

  • Cowan R, Jonard N (2007) Structural holes, innovation and the distribution of ideas. J Econ Interac Coord 2(2):93–110

    Article  Google Scholar 

  • David PA (1990) The dynamo and the computer: an historical perspective on the modern productivity paradox. AEA Pap Proc 80(2):335–361

    Google Scholar 

  • Elliott M, Golub B (2013) A network approach to public goods. In: Proceedings of the Fourteenth ACM Conference on Electronic Commerce. EC ’13 ACM New York, NY, pp 377–378

  • Falk I, Kilpatrick S (2000) What is social capital? A study of interaction in a rural community. Sociologica ruralis 40(1):87–110

    Article  Google Scholar 

  • Gambardella A, McGahan AM (2010) Business model innovation: general purpose technologies and their Implications for Industry Structure. Long Range Plan 43:262–271

    Article  Google Scholar 

  • Gould RV, Fernandez RM (1989) Structures of mediation: a formal approach to brokerage in transaction networks. Sociol Methodol 19:89–126

    Article  Google Scholar 

  • Hanifan LJ (1916) The rural school community center. Annals of the American Academy of Political and Social Science 67:130–138

  • Horn RA, Johnson CR (1994) Topics in matrix analysis. Cambridge University Press

  • Isham J, Kähkönen S (2002) How do participation and social capital affect community-based water projects? Evidence from Central Java, Indonesia. In: Grootaert C, van Bastelaer T (eds) The role of social capital in development: an empirical assessment. Cambridge University Press

  • Jackson MO, Zenou Y (2014) Games on Networks. In: Young P, Zamir S (eds) Handbook of game theory, vol 4. Elsevier Science

  • Ley E (1997) Optimal provision of public goods with altruistic individuals. Econ Lett 54(1):23–27

    Article  Google Scholar 

  • Motiram S, Osberg L (2010) Social capital and basic goods: the cautionary tale of drinking water in India. Econ Dev Cult Chang 59(1):63–94

    Article  Google Scholar 

  • Paldam M (2005) Social capital and social policy. In: Paper presented at New Frontiers of Social Policy Conference

  • Pargal S, Gilligan D, Huq M (2002) Does social capital increase participation in voluntary solid waste management? Evidence from Dhaka, Bangladesh. In: Grootaert C, van Bastelaer T (eds) The role of social capital in development: an empirical assessment. Cambridge University Press

  • Portes A (2000) The two meanings of social capital. Sociol Forum 15(1):1–12

    Article  Google Scholar 

  • Uzzi B, Spiro J (2005) Collaboration and creativity: the small world problem. Am J Sociol 111(2):447–504

    Article  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442

    Article  Google Scholar 

  • Wellman B (1979) The community question: the intimate networks of East Yorkers. Am J Sociol 84(5):1201–1231

    Article  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Bulat Sanditov.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sanditov, B., Arora, S. Social network and private provision of public goods. J Evol Econ 26, 195–218 (2016).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • Public goods
  • Interrelated utilities
  • Social capital
  • Social network analysis
  • Bonding and bridging
  • R&D networks

JEL Classification

  • H41
  • D85
  • O31