Cooperative project scheduling with controllable processing times: A game theory framework

This paper considers a project-scheduling environment assuming that the activities of the project network are distributed among a set of actors (or agents). Activity durations are modeled as time intervals and are controllable, meaning that every actor is allowed to shorten the duration of some activities by adding extra-money. For performing the project, actors have to collaborate with each other intending to satisfy a desired project duration. In this work, every actor´s payoff corresponds to a given ratio of the total customer´s payment, which itself depends on the ability of the actors to achieve the project in time, provided daily penalty costs are applied in case of tardiness. This problem can be modeled as a game, where players (actors) have to select a strategy (a duration vector for their activities) intending to maximize their profit. In this paper, the focus is put on the modeling of this project game, and on the connections between various decision problems, arising either in decision or game theory. We also study the particular case where each activity is assigned to one specific agent and a polynomial-time algorithm is proposed for finding Nash equilibrium with the smallest project makespan.