Irrelevance of private information in two-period economies with more goods than states of nature

We introduce a two-period economy with asymmetric information about the state of nature that occurs in the second period. Each agent is endowed with an information structure that describes her (incomplete) ability to prove whether or not a state has occurred. We show that if the number of states of nature is not greater than the number of goods, then, generically, the equilibria of the associated full information economy are also equilibria of the asymmetric information economy. The information structures of the agents are, in that sense, irrelevant.