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In this paper, we evaluate the scope of Chadwick’s claim on the superiority of competition for the market over competition in the market under incomplete information. We firstly characterize the expected outcome achieved under competition in the market at a Cournot Bayesian-Nash equilibrium. Then we characterize the optimal expected outcome achieved under a competition for the market mechanism designed by a government facing a shadow cost of public funds. We show that a regulated monopoly selected by an auction mechanism results in higher expected welfare than does duopoly competition when the entry cost is low but that the opposite holds when the market size is small and the entry cost is high for some values of the shadow cost of public funds. These results are explained by the influence of adverse selection on the entry decision at the Cournot equilibrium and by the level of expected total fixed costs in both mechanisms. Copyright Springer Science+Business Media, LLC 2007