A remark on the continuity of the Walras correspondence in pure exchange economies

Abstract

We revisit a classical theme of general equilibrium theory, namely the continuity of the Walras correspondence. Using a remarkable theorem due to Fort (Publ Math Debr 2:100-102, 1951) which has widely been used in recent literature on game theory, we prove the generic continuity of the price equilibrium-set correspondence under very general assumptions on the exchange economy.

On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space

“…We extend their results taking into consideration infinite dimensional commodity spaces and by characterizing stability when the continuity property in the equilibrium correspondence can not be obtained directly. In fact, our results answer the question posited in Dubey and Ruscitti (2015) about the possibility of getting stability results in infinite dimensional economies. In ad-dition we remark that we have not restricted the economies to have the same space of agents as it has typically been done in the literature.…”

“…Recently, the continuity of the equilibrium correspondence in general equilibrium theory was stated by Dubey and Ruscitti (2015) and He et al (2017). We extend their results taking into consideration infinite dimensional commodity spaces and by characterizing stability when the continuity property in the equilibrium correspondence can not be obtained directly.…”

“…In the second case, the set of agents is assumed fixed (see Carbonell-Nicolau (2010) or Correa and Torres-Martínez (2014)). Notice that even if we only consider economies with finitely many agents and an infinite dimensional commodity space, essential stability is not ensured (See Dubey and Ruscitti (2015), p. 2). In addition, we add uncountable varying sets of agents.…”