Core rationalizability in two-agent exchange economies.
This is an interesting paper that continues the author' (especially the second author's) investigations on the collective rational choice in a two-agent exchange economy. The standard issue considered in the literature is the rationalizability of collective choice by means of a single social ordering. The problem analyzed in this paper deviates from the standard framework and investigates whether the observed social choices can be rationalized by a profile of individual preference relations rather than a single social ranking. To this question, the work of \textit{Y. Sprument} [J. Econ. Theory 93, 205--232 (2000; Zbl 0976.91014)] obtains existence conditions of preference profiles that generate observed choices as Nash equilibria or as Pareto efficient outcomes. The present paper provides, in the context of a two-agent exchange economy, necessary and sufficient conditions for the observed selections to be rationalized in terms of the core elementa generated by a profile of individual preferences with standard properties. The authors propose four axioms for characterizing the core rationalizability: Regularity, Persistence, Strict Path Monotonicity, and Strict Averaging Reduction. These axioms are shown to be independent and to provide necessary and sufficient conditions for the core rationalizability of a selection correspondence in a two-agent exchange economy, determining uniquely its rationalizing profile. For the case of two-agent, the core rationalizability coincides with the set of Pareto efficient and individually rational allocations, while the general \(n\)-agent case still remains a difficult, open problem. A helpful comparison between the present approach and [Sprumont loc. cit.] is discussed. Since the core of the rationalized observed selections is the subset of the Pareto set of efficient allocations, the present paper studies equivalent conditions for the core stable choices of commodity allocations from fixed feasibility sets, while [Sprumont loc. cit.] analyzes necessary conditions for rationalizing the Pareto efficient choices of abstract alternatives from varying feasible sets.
scientific article; zbMATH DE number 1850400