Francetich, A., "Stochastic Orders and Surplus-Rent Trade-Offs"
When designing a contract, a profit-maximizing principal trades off social surplus for lower information rents due the agent. Imagine that the principal can influence the distribution of agent types; for instance, a monopolist can invest in a marketing campaign to boost demand. Changes in the type distribution that generate more social surplus, however, may not be profitable for the principal if they lead to even higher information rents. When are the social and private benefits of a shift in the type distribution aligned?
In a quasilinear setting, I adapt Proposition 2 in Hart and Reny (2015) to show that a sufficient condition is for the type distribution to shift in the sense of first-order stochastic dominance (FOSD). With linear utilities, I propose a weaker stochastic order: incentive order dominance (IOD), i.e. dominance in the increasing convex order (ICxOD) applied to (possibly-truncated, possibly-ironed) virtual utilities. It turns out that, while weaker, IOD is “very close” to FOSD: For regular distributions, FOSD is in fact equivalent to ICxOD on the (non-truncated) virtual utilities.is "very close" to FOSD: We show that, for regular distributions, FOSD is in fact equivalent to ICxOD applied to the non-truncated virtual utilities.
Francetich, A. and B. Schipper, "Rationalizable Screening and Disclosure Under Unawareness" (R&R at the Journal of Economic Theory)
We analyze a principal–agent procurement problem in which the principal (she) is unaware of some of the agent’s (he) marginal cost types. The agent may have an incentive to raise the principal’s awareness—fully or partially—before a contract menu is offered, an action that may itself be informative about his type. We capture the principal’s reasoning in a discrete concave model via rationalizability, imposing restrictions on marginal beliefs over types such as log-concavity, reverse Bayesianism, and a mild assumption of caution.
We show that if the principal is ex ante unaware only of high-cost types, all of these types have an incentive to raise her awareness of them—otherwise, they would not be served. With three types, the two lower-cost types that the principal is initially aware of also prefer to raise her awareness of the high-cost type: their quantities suffer no additional distortions, and they both earn an extra information rent. Intuitively, the presence of an even higher-cost type makes the original two look better. However, with more than three types, it is possible for a type that the principal is initially aware of to find himself no longer being served after raising awareness about higher-cost types—in which case raising the principal’s awareness might cease to be profitable in the first place. When the principal is ex ante unaware only of more efficient (low-cost) types, no type raises her awareness, leaving her none the wiser.
Francetich, A. and B. Schipper, "Discrete Screening"
In this companion paper, we consider a principal who wishes to screen an agent with discrete types by offering a discrete menu of quantities and transfers. We assume that the principal’s valuation is strictly discretely concave and employ a discrete first-order approach. The agent’s cost types are modeled as non-integer, with integer types as a limiting case. This modeling choice allows us to replicate the usual constraint-simplification results and thus to emulate the well-trodden steps of screening under a continuum of contracts.
We show that the solutions to the discrete first-order conditions need not be unique even under strict discrete concavity. However, there can be no more than two optimal contract quantities for each type, and—if there are two—they must be adjacent. Moreover, we can ensure only weak monotonicity of quantities even when virtual costs are strictly monotone, unless we restrict the ``degree of concavity'' of the principal’s utility. We introduce a rationalizability notion robust to variations in beliefs over types, called Delta-O Rationalizability, and show that the set of Delta-O rationalizable menus coincides with the set of standard optimal contracts—possibly augmented to include irrelevant ones.
Francetich, A., C. Frosi, and A. Gambardella, "Managerial vs. Statistical Spillover in Business Strategy" (R&R at the Strategic Management Journal)
Our paper (formerly titled ``Strategic Selection of Business Activities: Statistical vs. Managerial Spillover'') analyzes the problem of selecting a portfolio of business activities given a budget constraint and featuring value spillover across activities. Key factors in this selection process are the synergies across activities. We develop a model that analyzes the implications of two types of synergies: \textit{managerial spillover}, well-studied synergies that stem from the exploitation of common resources or real assets, and \textit{statistical spillover}, largely overlooked synergies whereby news on the value of one activity are informative about the value of others. This distinction has tangible implications for business strategy. Economies of joint production imply that, in order to exploit managerial spillover, activities must be assessed and undertaken in blocks, under centralized management. Statistical spillover allows for activities to be assessed and undertaken under decentralized management provided that all relevant value information is shared across units. Thus, statistical spillover is consistent with decentralized management but integrated information.