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 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.