Conservation auctions allow landholders to propose conservation projects and associated payments (bids) for consideration by a conservation agency. Recently, the application of iterative combinatorial auction designs has been proposed to improve outcomes of conservation auctions. In combinatorial auctions, landholders are allowed to offer projects each of which involves activities aimed at providing one or multiple services. An iterative format allows bidders the opportunity to gradually explore the type of projects they want to offer, with this process being facilitated through price feedback provided based on intermediate auction round results. Auction designs vary with the type of feedback and respond differently to market conditions. At present there is a lack of information about their performance in markets with varying degrees of competition (in terms of number of bidders and level of target). Therefore, using an agent‐based simulation model, we evaluate a number of iterative auction designs. We observe that a higher degree of competition leads to a higher auction efficiency. In a high competition environment, efficiency outcomes tend to be less sensitive to auction design choices. Therefore, an auctioneer could enjoy freedom in design choice if adequate competition could be ensured. In weak competition environments, however, some auction designs perform better than others.