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 incum-bents 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 anentrycostof$1. Ifentrantenters,sheenterswithsu?cientcapacitytoserveentiremarket.

1. In the ?rst round, the incumbent alone is in the market. Incumbent sets a price and buy-ers choose to buy or not according to their surplus. Entrant can observe the price charged by incumbent.

2. In round two, entrant decides to enter market.

3. If entrant does not enter, incumbent sets price, buyers choose, game ends. If entrant enters, both incumbent and entrant set price simultaneously.

Might incumbent want to signal its cost position to entrant? Is there a way to do so using the price in the ?rst round?