In the context of supply function competition with private information, we test in the laboratory whether—as predicted in Bayesian equilibrium—costs that are positively correlated lead to steeper supply functions and less competitive outcomes than do uncorrelated costs. We find that the majority of subjects bid in accordance with the equilibrium prediction when the environment is simple (uncorrelated costs treatment) but fail to do so in a more complex environment (positively correlated costs treatment). Although we find no statistically significant differences between treatments in average behaviour and outcomes, there are significant differences in the distribution of supply functions. Our results are consistent with the presence of sophisticated agents that on average best respond to a large proportion of subjects who ignore the correlation among costs. Experimental welfare losses in both treatments are higher than the equilibrium prediction owing to a substantial degree of productive inefficiency