["Bulletin of Economic Research, Volume 78, Issue 2, Page 358-367, April 2026. ", "\nABSTRACT\nWe study the existence of equilibrium when agents' preferences may not be convex. For some specific utility functions, we provide a necessary and sufficient condition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single‐valued nor convex‐valued."]