Francetich, A., "A Stochastic Order For Incentives"
When designing a contract, a profit-maximizing principal trades off social surplus against information rents. Shifts in the type distribution that generate more surplus 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?
I propose a stochastic order, incentive order dominance (IOD), as the minimal stochastic order that ensures monotonicity of the principal’s profit over the class of continuous, non-decreasing, and convex cost functions. IOD consists of applying dominance in the increasing convex order (ICxOD) to possibly-ironed virtual utilities truncated below 0. I show that IOD is strictly weaker than FOSD. Surprisingly, however, it is not “that much weaker”: For regular distributions, FOSD is in fact equivalent to ICxOD on the untruncated virtual utilities. I also identify weaker stochastic orders for some smaller cost-function classes.
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, "Screening with Discrete Types and Discrete Contracts" (Under Review)
We study screening when both the agent’s types and the contracts available to the principal are finite: Quantities and transfers are drawn from a finite integer grid, while marginal costs lie on a slightly off-set grid, with integer costs as a limit case. We compare two solution concepts, equilibrium and rationalizability. Since rationalizability does not feature an equilibrium tie-breaking convention, we analyze screening under weak and under strict incentives. We develop a discrete first-order approach and characterize the optimal menus for full-support log-concave beliefs. Optimal quantities need not be unique, but at most two adjacent quantities are optimal and multiplicity is a knife-edge case in beliefs. Our rationalizability solution concept, ∆-O rationalizability, restricts the principal’s beliefs over types and requires her best replies to be robust to belief perturbations. Two rounds of elimination suffice, and the rationalizable and the equilibrium outcomes essentially coincide: The predictions of equilibrium survive without a common prior, while avoiding a tie-breaking convention.
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: managerial spillover, well-studied synergies that stem from the exploitation of common resources or real assets, and 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.