Mean consumption representation of consumption externalities

The author previously investigated exchange economies with a price-dependent reference coalition externality which can be represented as a mean consumption bundle of a reference coalition C [Noguchi, M., 2005. Interdependent preferences with a continuum of agents. Journal of Mathematical Economics 41, 665–686]. In the present paper, we justify, under a suitable generalization of the notion of negatively interdependent preferences [Ok, E.A., Koçkesen, L., 2000. Negatively interdependent preferences. Social Choice and Welfare 17, 533–558], that consumers act as if they compute the mean consumption bundle ∫CxdμC of C and maximize an appropriate utility function V whose consumption externality depends only on ∫CxdμC. The strong law of large numbers plays a crucial role in our arguments.