Information and size of coalitions

We consider a set of asymmetrically informed agents, where the information of each trader is susceptible of being altered when she becomes a member of a coalition. For this, we consider a general rule that depending on the coalition, a signal (or an information partition) is assigned to each member of the coalition. We set examples showing that Grodal’s (Econometrica 40:581–583, 1972), Schmeidler’s (Econometrica 40:579–580, 1972) and Vind’s (Econometrica 40:585–586, 1972) core characterizations of a continuum economy may fail in this general informational setting. However, under mild assumptions on the rule, we extend Schmeidler’s and Vind’s results to economies that allocate information to agents in each coalition according to the rule. We then focus on information mechanisms based on the size of coalitions and provide a general characterization result for the corresponding cores. Moreover, we pay close attention to the rule that assigns the shared information to each member of specific coalitions. We prove that the resulting cores are exactly the same independently of whether arbitrarily small or large coalitions share information.