Seminario "Stochastic Orders and Incentives"
Miércoles 17/6, 17.15h
Presentado por Alejandro Francetich
Abstract
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.
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.
Alejandro Francetich
Ph.D. in Economic Analysis and Policy, Stanford GSB, Stanford University. Associate Professor, School of Business, University of Washington Bothell. His research interest is Microeconomic Theory, in particular Mechanism Design.