Finding an optimal Nash equilibrium to the multi-agent project scheduling problem

Abstract

Cooperative projects involve a set of self-interested contractors, each in charge of a part of the project. Each contractor may control the duration of his activities, which can be shorten up to an incompressible limit, by gathering extra resources at a given cost. In this context the resulting project makespan depends on all contractors' decisions. The client of the project is interested in a short project makespan. As an incentive, the client offers a daily reward to be shared among the contractors in order to complete the project earlier than expected. In practice, either the reward sharing policy results from an upfront agreement or payments are freely allocated by the client himself. Each contractor is only interested in the maximization of his own profit, and behaves accordingly. This paper addresses the problem of finding a Nash equilibrium and a sharing policy that minimize such project makespan while ensuring its local stability. We explain how the resulting problem, which is NP-hard, can be modeled and solved with mixed integer linear programming (MILP). A computational analysis on large instances proves the effectiveness of our approach. Useful insights are also derived from an empirical investigation of the influence of reward sharing policy, for a better understanding of how a project customer should make the most of his funds in such project management context.