Credit market segmentation, essentiality of commodities, and supermodularity

We consider incomplete market economies where agents are subject to price-dependent trading constraints compatible with credit market segmentation. Equilibrium existence is guaranteed when either commodities are essential, i.e, indifference curves through individuals' endowments do not intersect the boundary of the consumption set, or utility functions are concave and supermodular. The smoothness of mappings representing preferences, financial promises, or trading constraints is not required. Hence, we may include in our framework economies where ambiguity is allowed and agents maximize the minimum expected utility over a set of priors, or where markets include non-recourse collateralized loans.