Integer Programming Methods to Identify Nash Equilibrium Solutions for Platform-Based Scheduling Games

This paper proposes an integer programming approach to examining Nash equilibrium solutions of a game modeling freelancer platforms. This Platform-Based Scheduling Game is played by the clients who choose a single freelancer that processes their jobs and the freelancers create a schedule of work based on the clients who choose them and their preferences. In order to identify a Nash equilibrium schedule, a schedule in which no clients change their choice of freelancers based on every other client’s choice, integer programming is utilized. We create a set of integer programming constraints where there exists a one-to-one correspondence between a Nash equilibrium of the game and a feasible solution to the integer program. The one-to-one correspondence allows the integer program to find the optimal Nash equilibrium schedules for objectives that model the considerations of the platform, freelancers, and clients. It also allows us to precisely calculate the price of anarchy and price of stability, and evaluate the loss in objective function value for one stakeholder of the game when the game is optimized for another stakeholder. We show that the decentralized matching performs well for the clients and the freelancers compared to the centralized optimal matching (that arises when we do not consider the clients as independent decision-makers) but the platform can suffer heavily from allowing clients autonomy in their decision making.