A Bayesian approach to continuous type principal-agent problems |
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| Institution: | 1. Isenberg School of Management, University of Massachusetts-Amherst, 90 Campus Center Way, 209A Flint Lab, Amherst, MA 01003, USA;2. Management School, University of Liverpool, L69 7ZH, UK;3. Lancaster University Management School, LA1 4YX, UK;1. HEC Liège, Management School of the University of Liège, Liège, Belgium;2. School of Business and Economics, Maastricht University, Maastricht, the Netherlands;1. Department of Economics and Business, University of Catania, Corso Italia, 55, 95129, Catania, Italy;2. Portsmouth Business School, Centre for Operational Research and Logistics (CORL), University of Portsmouth, Portsmouth, United Kingdom;1. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern 67663 Germany;2. CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal;1. Universidade Federal do Paraná, Campus Avançado de Jandaia do Sul, Rua Doutor João Maximiano 426, Jandaia do Sul, Paraná 86900-000, Brazil;2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Avenida Trabalhador São-carlense 400, São Carlos, São Paulo 13566-590, Brazil;3. School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia;4. Departamento de Matemática, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs – Campus Universitário, Viçosa, Minas Gerais 36570-000, Brazil;1. Lancaster University Management School, LA1 4YX, UK;2. Athens University of Economics and Business, Athens 10434, Greece;1. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA;2. Department of Industrial Engineering and Management Systems, University of Central Florida, 12800 Pegasus Dr., Orlando, FL 32816, USA;3. Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA 15261, USA |
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| Abstract: | 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. |
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