Optimal contracting in networks

We study optimal contracting between a firm selling a divisible good that exhibits positive externality and a group of agents in a social network. The extent of externality that each agent receives from the consumption of neighboring agents is privately held and is unknown to the firm. By explicitly characterizing the optimal multilateral contract, we demonstrate how inefficiency in an agent's trade propagates through the network and creates unequal and network-dependent downward distortion in other agents' trades. Furthermore, we describe bilateral contracts (non-linear pricing schemes) and characterize their explicit dependence on the network structure. We show that the firm will benefit from uncertainty in an agent's valuation of other agents' externality. We describe the profit gap between multilateral and bilateral contracts and analyze the consequences of the explicit dependence of the contracts on network structure. When the network is balanced in terms of homogeneity of agents' influence, network structure has no impact on the firm's profit for bilateral contracts. On the other hand, when the influences are heterogeneous with high dispersion (as in core-periphery networks) the restriction to bilateral contracts can result in profit losses that grow unbounded with the size of networks.