Nash-profit efficiency: A measure of changes in market structures

• Efficiency is estimated in an imperfectly competitive market with endogenous price.
• A direction toward Nash solution is suggested in the directional distance function (DDF).
• Nash-profit efficiency (NPE) is developed for measuring the changes in market structures.
• The proposed NPE is compared with the typical profit efficiency.
• An empirical study of the oil and natural gas industry in New York State is conducted.

Imperfectly competitive markets can be characterized by endogenous prices, limited or no competition, and the exercise of market power. To address the resulting dysfunctionality, this study proposes an alternative efficiency measure estimated by the directional distance function (DDF) with the direction toward Nash equilibrium, and develops the Nash-profit efficiency (NPE) and its decomposition which complements the typical profit efficiency measure. We model the production possibility set and the price functions of inputs and outputs, and then develop the mixed complementarity problem (MiCP). We validate the model with an empirical study of the oil and natural gas industry in New York State between 1981 and 1989. The results show that before 1984, firms exploited a less competitive market; that between 1984 and 1986, the number of new entrants transformed the market; and that after 1986, no firms could exercise market power due to market restructuring (deregulation) and an unforeseen oil glut. Based on the results, we conclude that the direction toward Nash equilibrium can be justified for efficiency estimation in imperfectly competitive markets, and that NPE is appropriate for investigating changes in market structures.