Consistency Requirements and Pattern Methods in Cost Sharing Problems with Technological Cooperation

In the cost sharing model with technological cooperation, we investigate the implications of a number of consistency requirements. In a context where the enforcing authority cannot prevent agents from splitting or merging their demands (in order to reduce their cost shares), the methods used must make such manipulations unprofitable. The paper introduces a family of rules that are immune to these demand manipulations, the pattern methods. For each of these methods, the associated production pattern indicates how to use the different technologies in order to meet the agents demands. Within this family, two rules stand out: the public Aumann-Shapley rule never rewards technological cooperation; and the private Aumann-Shapley rule generates the maximum technological rent for homogeneous problems. The paper also studies the sharing methods that are immune to manipulations of the technology. A useful axiomatization of the public Aumann-Shapley rule ensues: it is the unique flow method that is immune to demand maneuvers and technology manipulations.