Price competition among electric vehicle (EV) charging stations is as fierce as the competition among gas stations. Nash equilibrium (NE) is a solution concept that can characterize a competition’s efficient and stable state. However, calculation of the equilibrium is often time-consuming and requires complete information on the charging stations. Rapidly changing charging stations often hinder reaching equilibrium. In this study, we analyze price competition with service capacity constraints and use an ordinal potential game framework to investigate the structure of the competition. By constructing the ordinal potential function, the equilibrium characterization is converted to identifying the solution through a single-objective optimization. We further propose a decentralized algorithm to enable effective price coordination to achieve equilibrium with maximized social welfare. To preserve the privacy of charging stations from internal collusion and external attacks, an advanced secure multi-party computation technology known as the Paillier Cryptosystem is customized for our proposed decentralized algorithm. Numerical studies based on field data suggest the significance of our framework.