Mixed-strategy Nash equilibrium in data envelopment analysis

In a typical productivity analysis, the efficiency measure assumes a perfectly competitive market with an endogenous price and depends on a fixed orientation with respect to a specific firm, such as an input-oriented measure. When an imperfectly competitive market affects the endogenous price, however, firms may take a “mixed strategy” approach to address uncertain competition. This study proposes a Mixed Strategy Measure (MSM). We construct a model embedded with a data envelopment analysis (DEA) framework, that identifies the mixed-strategy Nash equilibrium in the first stage and considers a probabilistic and multi-oriented efficiency measure in the second stage. Based on the environmental regulation and a typical Nash measure, we create two indices - environmental consistency and strategic consistency - to support the business roadmap development. We validate the proposed MSM with an empirical study of China's electric power industry. The results find that the proposed MSM complements the Nash measure, and the MSM model successfully supports our two managerial strategies: invest in capacity expansion or develop emission abatement technology.