On the stability of network structures with public goods

This paper explores the formation of stable network structures in a model with public goods. The multiplicity of equilibria in the non-cooperative formulation of network formation games brings out further difficulties in analyzing stability of network structures. This contrasts with the cooperative game approach where payoffs for agents are predetermined and thereby the multiplicity of equilibrium issues are sidestepped. We took issue with the multiplicity of equilibrium effort levels exerted on a given network structure, and we suggested different stability definitions for such network structures under multiplicity of equilibria. We demonstrated how these stability notions work for the network structures with four agents where breaking and forming links is costless, and the cost of exerting effort level is linear.