A game theoretical approach to sharing penalties and rewards in projects

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary nondecreasing reward and penalty functions on the total expedition and delay, respectively. Attention is focused on how to divide the total reward (penalty) among the activities: the core of a corresponding cooperative project game determines a set of stable allocations of the total reward (penalty). In the definition of project games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of the reward (penalty) function at hand. It turns out that project games are related to bankruptcy and taxation games. This relation allows us to establish the nonemptiness of the core of project games.