Non fixed-price trading rules in single-crossing classical exchange economies

Abstract

This paper defines the single-crossing property for two-agent, two-good exchange economies for classical (i.e., continuous, strictly monotonic, and strictly convex) individual preferences. Within this framework and on a rich single-crossing domain, the paper characterizes the family of continuous, strategy-proof and individually rational social choice functions whose range belongs to the interior of the set of feasible allocations. This family is shown to be the class of generalized trading rules. This result highlights the importance of the concavification argument in the characterization of fixed-price trading rules provided by Barberà and Jackson (1995), an argument that does not hold under single-crossing. The paper also shows how several features of abstract single-crossing domains, such as the existence of an ordering over the set of preference relations, can be derived endogenously in economic environments by exploiting the additional structure of classical preferences.

Strategy proofness and Pareto efficiency in quasilinear exchange economies

“…However, the generalization of the Momi (2013) result to the entire domain of classical preferences 3 An SCF is non-bossy if each agent is unable to affect the allocation of others whenever his change in preference does not affect his own allocation. 4 See also Goswami (2011b) for another recent contribution to the literature on strategy proofness on a single-crossing domain.…”

“…As mentioned in the Introduction, single-crossing domains are important in information economics, but have not been adequately analyzed in mechanism design. Exceptions are Saporiti (2009), who considers a model with finite set of alternatives, and Goswami (2011b), who looks at one-dimensional (i.e., two-good) models. Single-crossing domains present serious difficulties for mechanism design in economic environments; specifically, they do not permit Maskin monotonic (MM) transformations.…”