original papers : Uniqueness of Arrow-Debreu and Arrow-Radner equilibrium when utilities are additively separable

This survey paper has three purposes: We first present in finite dimension, different approaches to the problem of uniqueness of Arrow-Debreu equilibrium when agents have additively separable utilities. We then study how, in the specific framework of a two period contingent good economy the results obtained generalize to infinite dimension. We consider economies where agents' consumption space is $L^p_+ (\mu)\; 1 \leq p \leq \infty$ and agents' utilities are additively separable. Lastly, we show that in some restricted settings, some results may be used to prove uniqueness of Arrow-Radner equilibria when there are incomplete financial markets.