As water extractions from the world's rivers have grown, flows available for the environment have dwindled. In many parts of the world governments are now considering strategies to restore environmental flows. One strategy is for a government to buyback water from irrigators for the environment with annual lease arrangements. In this paper we have studied the role of market competition (in terms of environmental water demand and number of sellers) in determining the performance of multi-round environmental water buyback auctions using a stylized agent based simulation model. The results suggest that rent extraction lowers as the number of bidders increase and water demand decreases. However, we find significant differences in the way changes in demand and supply influence rent extraction. Reduction in water demand has much greater impact on rent extraction than increasing the number of bidders in the market. Further, in wet years (when supply is abundant relative to demand) bidders engage in more competitive bidding compared to cases in dry years. Results from the analysis indicate that government agencies benefit more from arranging buyback tenders (1) with a small target relative to tenders with a large bidder population and (2) with greater opportunities for the bidders to learn from the market in wet years compared to dry years.