Set-valued DEA production games

• DEA can be used to evaluate and distribute the benefits of cooperation in a production context.
• When output prices are unavailable (e.g. public services), outcomes are vector-valued.
• A set-valued cooperative game theory approach is proposed to handle this scenario.
• Models for computing Dominance and Preference Least Core allocations are formulated.

In this paper, a generalization of the linear production model is considered on the basis of a DEA-inspired technology in which the maximization of the production levels is formulated as a multi-objective linear programming problem. When multiple decision-makers cooperate by pooling their resources and sharing their technologies in the production process, the final production must then be divided between the agents involved, and a multi-commodity game arises. Such a game is referred to as a set-valued DEA production game. It is shown that, by adopting two different excess functions to measure the dissatisfaction of the coalitions, two different core concepts emerge, namely the preference core and the dominance core. Moreover, we provide the procedure to determine allocations in the respective least cores and show how to compute the nucleolus in the case of the excess function leading to the preference core. Finally, the results are illustrated with a case study.