Analysis of the impact of DMUs on the overall efficiency in the event of a merger

This paper addresses several mechanisms for overall ranking Decision Making Units (DMUs) according to the contribution of DMUs to the relative efficiency score of a merger considering aggregate units The possible organization of agents outside each possible merger naturally influences the relative efficiency score, which motivates the use of games in partition function form and specific ranking indices for DMUs based on the Shapley value. Several computational problems arise in their exact computation when the number of DMUs increases. We describe two sampling alternatives to reduce these drawbacks. Finally, we apply these methods to analyse the efficiency of the hotel industry in Spain