A Bayesian approach to continuous type principal-agent problems

Singham (2019) proposed an important advance in the numerical solution of continuous type principal-agent problems using Monte Carlo simulations from the distribution of agent “types” followed by bootstrapping. In this paper, we propose a Bayesian approach to the problem which produces nearly the same results without the need to rely on optimization or lower and upper bounds for the optimal value of the objective function. Specifically, we cast the problem in terms of maximizing the posterior expectation with respect to a suitable posterior measure. In turn, we use efficient Markov Chain Monte Carlo techniques to perform the computations

Sample average approximation for the continuous type principal-agent problem

The article of record as published may be found at http://dx.doi.org/10.1016/j.ejor.2018.12.032We develop a method for finding approximate solutions to the continuous agent type principal-agent problem when analytical methods are not available. The solution is calculated by solving a discrete agent type version of the problem using sample average approximation and bootstrapping. We show how a solution to the approximate problem can be used to derive a lower bound and expected upper bound for the optimal objective function, and evaluate the error associated with the approximation. Numerical examples illustrate convergence in the approximate solution to the true solution as the number of samples increases. This works yields a method for obtaining some tractability in continuous type principal-agent problems where solutions were previously unavailable.National Science Foundation grant CMMI-153583