It is well known that software development projects tend to be based on over-optimistic cost estimates. Better knowledge of the sources of this over-optimism is necessary to improve realism in software development project bids and budgets. This paper analyses the effect of "the winner?s curse". The winner?s curse is a result of the selection of software providers among those with the lowest bid, i.e., those with a tendency towards the highest level of over-optimism. The winner?s curse has not been extensively analyzed in software cost estimation studies, but is a well known phenomenon in domains such as auctioning. We exemplify the effect of the winner?s curse with data from a real software development bidding round and simulate how increase in number of bidders and cost uncertainty impact the expected profit. We argue that the winners? curse is a problem for both clients and providers, and that it may lead to inefficient use of scarce resources. Possible remedies for reduction of negative effects of the winner?s curse are discussed.