TY - JOUR
AU - Cole,Harold L.
AU - Kubler,Felix
TI - Recursive Contracts, Lotteries and Weakly Concave Pareto Sets
JF - National Bureau of Economic Research Working Paper Series
VL - No. 17064
PY - 2011
Y2 - May 2011
DO - 10.3386/w17064
UR - http://www.nber.org/papers/w17064
L1 - http://www.nber.org/papers/w17064.pdf
N1 - Author contact info:
Harold L. Cole
Economics Department
University of Pennsylvania
3718 Locust Walk
160 McNeil Building
Philadelphia, PA 19104
Tel: 215-898-7788
E-Mail: colehl@sas.upenn.edu
Felix Kubler
University of Zurich
Plattenstrasse 32
CH-8032 Zurich
Switzerland
E-Mail: fkubler@gmail.com
AB - Marcet and Marimon (1994, revised 1998, revised 2011) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a flat region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through - one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal's choice set is not convex but where randomization is possible.
ER -