Game theoretical model of DEA efficiency

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalized DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalized convex cone constrained efficiency game model in assembling the generalized DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalized efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.