Coalitional fairness with participation rates

This paper investigates coalitional fairness in pure exchange economies with asymmetric information. We study allocations of resources which are immune from envy when comparisons take place between coalitions. The model allows negligible and non-negligible traders, partially informed about the true state of nature at the time of consumption, to exchange any number, possibly infinite, of commodities. Our analysis is based on the Aubin approach to coalitions and cooperation. Namely, on a notion of cooperation allowing traders to take part in one or more coalitions simultaneously, employing only shares of their endowments (participation rates). We introduce and study in detail the notion of coalition fairness with participation rates (or Aubin c-fairness) and show that flexibility in cooperation permits to recover the failure of fairness properties of equilibrium allocations. Our results provide applications to several market outcomes (ex-post core, fine core, ex-post competitive equilibria, rational expectations equilibria) and emphasize the consequences of the convexification effect due to participation rates for models with large traders and infinitely many commodities.