Bargaining game model in the evaluation of decision making units

Data envelopment analysis (DEA) has been proven an effective tool for performance evaluation and benchmarking, which can provide a relative efficiency measure for peer decision making units (DMUs) with multiple inputs and outputs. Nevertheless, its flexibility in weighted inputs and weighted outputs as well as its nature of self-evaluation has been criticized. The cross-evaluation method is developed as a DEA extensive tool being utilized to identify the best practice DMUs and to rank all DMUs using cross-efficiency scores that are associated with all DMUs, however, it still seems imperfect since the non-uniqueness of cross-efficiency measure possibly derogates the practicability of this method, and especially, the average cross-efficiency measure is not a Pareto one, so not all DMUs have the motivation to accept it. In this paper, we adopt a Nash bargaining game to improve the usual cross efficiency evaluation method. In the game, each DMU will be an independent player, and the bargaining solution between CCR efficiency and cross-efficiency can be obtained by using the classical Nash bargaining game model. The advantage of the bargaining efficiency lies on that it is a Pareto one and all the DMUs will have motivation to accept it, as well as that the adoption of common weights in evaluation will result in the equitableness of ranking all DMUs. Finally, the comparisons of those efficiency scores mentioned above and the corresponding weights are demonstrated by an example of R&D project selection.