Network public goods with asymmetric information about cooperation preferences and network degree

We propose a game theoretical model of one-shot network public goods formalizing the ‘closure argument’ that cooperation is more frequent in denser groups or networks. Equilibrium analyses show that (i) an ‘inefficiency problem’ exists: players all preferring mutual cooperation need not all cooperate; (ii) in dyads, groups and networks with degree independence, first order stochastic dominance shifts of the distribution of cooperation preferences or the degree distribution (weakly) increases cooperation, and (iii) the latter result does not hold for networks with degree dependence. Hence the closure argument always holds in networks satisfying degree independence but not in other networks.
Keywords: Network public goods, Asymmetric information, Co-operation, Closure, Degree dependence, Social exchange heuristic