A consignment auction aims to increase political feasibility by reducing the financial burden of initial permits allocation and to do the role of price discovery. However, previous analytical models presented contradictory results for the price discovery function of a consignment auction. Thus, this study reexamines whether a consignment auction can perform its price discovery function. The study uses a simple game model with several assumptions differentiated from previous analytical models: explicit consideration of the secondary market and firms as price-takers with various behaviors to respond to uncertainty about the price in the secondary market. Firms are classified into three types: speculators who seek arbitrage, doctrinarians who determine a permit demand based on an estimation of their marginal abatement cost, and neutralists who keep a permit demand the same as initial emission endowments. The results reveal that when a consignment auction was introduced, the expected equilibrium price was identical to that of the secondary market price, demonstrating that the auction could deliver the price discovery function. This is because speculators and doctrinarians provide information about their price expectations and marginal abatement cost through their estimated demand functions. Additionally, the smaller number of neutralists is, and the higher the risk-seeking propensity of speculators is, the more effective the price discovery function is.