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Abstract We investigate the fairness property of equal-division competitive market equilibria (CME) in asymmetric information economies with a space of agents that may contain non-negligible (large) traders. We first propose an extension to our framework of the notion of strict fairness due to Zhou (J Econ Theory 57:158–175, 1992). We prove that once agents are asymmetrically informed, any equal-division CME allocation is strictly fair, but a strictly fair allocation might not be supported by an equilibrium price. Then, we investigate the role of large traders and we provide two sufficient conditions under which, in the case of complete information economies, a redistribution of resources is strictly fair if and only if it results from a competitive mechanism.