First offers are powerful anchors that strongly determine the outcome of a negotiation. To gain deeper insights into the power of first offers, we adopt a process-oriented view and analyze the impact of first offers on single subsequent concessions, in simulations of distributive price negotiations between a buyer and a seller. Using a multilevel approach which is new to this field of investigation, the results show that first offers have a significant influence on all subsequent concessions made by the buyer and seller, and these concessions decrease during the course of negotiation. Interestingly, concessions remain unaffected by the opponent’s preceding concession. These results thus demonstrate that the first offer is indeed a powerful anchor, as it influences all single steps required to reach an agreement.