We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation to set up a principal/agent contract theory model where the principal faces a large population of agents interacting in a mean field manner. We reduce the problem to the optimal control of dynamics of the McKean-Vlasov type, and we solve this problem explicitly for a class of models with concave rewards. The paper concludes with a numerical example demonstrating the power of the results when applied to an example of epidemic containment.
All Science Journal Classification (ASJC) codes
- Strategy and Management
- Management Science and Operations Research
- Epidemic control
- Mean field game
- Principal agent problem