We show that when bankruptcy, subject to penalties, is allowed, it is possible to prove the existence of equilibrium in a model with a continuum of states without imposing any assumptions on ex-post endowments.

In this paper, we introduce a perfect competition test which checks the incentives of arbitrarily small coalitions to behave strategically in endowments and preferences. We apply this coalitional incentive compatibility test to atomless economies with a continuum of differentiated commodities....

We study a two periods model of incomplete markets with nominal assets unsecured by collateral, where agents can go bankrupt but there are no bankruptcy penalties entering directly in the utility function. We address two cases: first, a proportional reimbursement rule under bounded short sales...