An incumbent and entrant face a market of 100 buyers. Each buyer has a RP of $100 for the incumbents as well as entrants product. At each round each buyer is interested in buying no more than one unit of the product. The incumbent has a $40 per unit of cost of production that is private information, i.e., the entrant does not know what the incumbents actual production costs are. The entrant does have a guess. Entrant believes that incumbents costs are either $40 per unit or $60 per unit (she assigns positive probability to either possibility and entertains no other possibilities). Incumbent knows entrants beliefs, entrant knows that incumbent knows and so on. Entrants costs are $50 per unit and incurs anentry cost of $ 1.
Question: Might incumbent want to signal its cost position to entrant? Is there a way to do so using the price in the first round?