The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals; this is the case even if the asset market is incomplete.
Kubler, F., & Polemarchakis, H. M. (1999). The identification of preferences from the equilibrium prices of commodities and assets (CORE Discussion Papers 1999/33). https://hdl.handle.net/2078.5/33554