Case $3$: One Chinese trading company intended to export bicycles to U$.$S$.$ The salesmen made an offer on July $15$ to some American merchant, subject to reply reaching the offeror by the end of August. The price was $5000$ bicycles at USD $80$ per unit FOB Shanghai, shipment to be made during Oct. The American merchant replied on July $18,$ expressing his acceptance of the offer but asking for $10\%$ discount on the price. The Chinese salesmen didn't reply, and sold the bicycles to others. While on July $28,$ he received a fax from the American merchant stating that the latter accepted all the terms in the offer of July $15$ and expected the Chinese company to ship the goods in Oct. The sale staff called back immediately, informing the American that the goods had already been sold out. However, the American merchant insisted that the contract had already been established and the Chinese should fulfill its obligations, otherwise he would file a claim.

According to the relevant international convention or custom, whether the contract has been established or not? Please make a judgment and give your reasons.