This paper uses the Hartman-Stampacchia theorems as primary tool to prove the Gale-Nikaido-Debreu lemma. It also establishes a full equivalence circle among the Hartman Stampacchia theorems, the Gale-Nikaido-Debreu lemmas, and Kakutani and Brouwer fixed point theorems.

An abundant literature is concerned with the existence of equilibrium in incomplete markets where participation to financial markets is not restricted. To mention a few, Cass (1984), Werner (1985), Geanakoplos and Polemarchakis (1986), Duffie (1987), Duffie and Shafer (1985) and Magill and...