关键词: DEA, 博弈, 交叉效率, 动态变化, 竞争, 合作

Abstract: Using DEA to evaluate relative efficiency, DMUs (decision making units) often needs to consider multiple objectives. The competitive and cooperative relationships between DMUs will also change with the change of objectives. Although the traditional competitive and cooperative model considers the situation that competition and cooperation between DMUs occur simultaneously, it ignores the dynamic change of competition and cooperation. Regarding the competitive and cooperative strategy as the breakthrough point, we introduce the priorities of multi-objective programming into the traditional game cross efficiency model, developing a multi-objective DEA game cross efficiency model, that is the DEA game cross efficiency model for dynamic change of competitive and cooperative relationships between decision making units. This model fully reflects the dynamic change of competition and cooperation between DMUs. Its focus is to find the optimal cross efficiency score directly rather than improve the problem of multiple optimal weights. Using this model, we evaluate the input-output efficiency of manufacturing in Yangtze River Delta region in 2014 under the constraints of environmental pollution. The analysis indicates that the DEA game cross efficiency model for dynamic change of competitive and cooperative converges more quickly than the traditional DEA game cross efficiency model, and its cross efficiency scores converge to a unique Nash equilibrium. Our model implicitly incorporates the relative importance of different objectives without the need for specifying the exact assurance regions.

Key words: DEA, game, cross efficiency, dynamic change, competitive, cooperative