Screening with Network Externalities

Abstract

Network externality is a prominent feature of increasingly many products: the marginal payoff of one’s consumption increases as his neighbors consume more. In- formation of network structure is important to the seller, but is often privately known to the buyers. We model a monopoly’s optimal pricing strategy to “screen” buyers’ network information: their susceptibility (out-degree) and influence (in-degree). Our main result is that susceptibility and influence have different effects on the optimal allocations and can be separated out in the optimal screening contracts. Specifically, we characterize the optimal allocations for both directed networks where each buyer’s susceptibility and influence are independent, and undirected networks where the two are identical. For directed networks, we show the optimal allocation only depends on a buyer’s susceptibility and exhibits simple forms with quadratic intrinsic value. We further contrast the analysis with two benchmarks – complete information pricing and uniform pricing – to shed light on the value of screening and the value of network in- formation. For undirected networks, we show the seller directly screens buyers on their susceptibility and indirectly condition the allocations on their inferred influence. We also extend the model to accommodate for (1) weak affiliation between a buyer’s susceptibility and influence, (2) the case in which the monopoly can incentivize influence with contingent contracts (referral bonuses), and (3) the situation in which susceptibility and influence are endogenous to the optimal allocations.