A Note on Principal-Agent Problem in a Stochastic System

Abstract

We consider a principal (e.g., a ridesharing platform such as Uber or Lyft) who receives two types of jobs (e.g., passengers requesting solo or shared rides) according to a Poisson process. The principal first decides which jobs to admit and then assigns an agent (e.g., driver) to perform them. The agent who is assigned the job has preference between the two types of jobs. The agent can independently decide whether to accept or reject a job which is assigned to them. The principal and the agent receive different rewards from each job thus resulting in incentives misalignment. The research questions are: (1) which job(s) should the principal admit? (2) How much should the principal pay the agent? To answer these questions, we model the agent as an M / M / 1 loss system. Using a Markov decision process and dynamic programming, we find the optimal wage the principal should pay the agent and a threshold admission policy (also known as trunk-reservation or switching-curve policy). Prior literature did not consider two players (agent and principal) with misaligned objectives and each making dynamic decisions. We contribute to the literature by adding another layer of decision making and by introducing server (agent) independence wherein the servers have preferences regarding the type of job they wish to perform.