Grouping Agents with Persistent Types
Employees are divided into grades. Toyota places suppliers into only a small number of categories. This paper shows that grouping of privately-informed and persistent agent types arises naturally in relational incentive contracts when agent type is continuous. Malcomson (Econometrica, 2016) showed that it is not possible to separate all such agent types if, following full revelation of an agent’s type, payoffs for principal and agent are on the Pareto frontier. This paper shows how much separation can be achieved with agent types for which first-best effort is unattainable. It first establishes necessary properties for a continuation equilibrium to be on the Pareto frontier. It then characterises the finest partitions of agent types with those properties. Separation may take time, with initial coarser partitions being subsequently refined, but does not continue indefinitely. When it stops, there remain a finite number of groups of agent types. The number of such groups can be calculated for constant elasticity cost of effort functions and is typically small despite agent type being continuous. For quadratic cost of effort, no separation is possible unless the discount factor is below 2/3. For a discount factor of 0.9, separation is possible only with much less convexity and even then the number of groups is no more than six or so unless there is almost no convexity, a promising characteristic for applications where the number of groups is small.
Date: 1 December 2020, 12:45 (Tuesday, 8th week, Michaelmas 2020)
Venue: Held on Zoom
Speaker: Jim Malcomson (University of Oxford)
Organising department: Department of Economics
Part of: Economic Theory Workshop
Booking required?: Not required
Audience: Members of the University only
Editor: Melis Clark