Reduced-Form Allocations with Complementarity: A 2-Person Case

TL;DR

This paper characterizes when reduced-form allocation probabilities are implementable in a two-person bargaining setting with complementarities, extending known results and providing new insights into barter and compromise problems.

Contribution

It offers a necessary and sufficient condition for implementability in a two-agent bargaining problem with complementarities, highlighting differences from Border's theorem.

Findings

Derived a new implementability condition for two-person bargaining with complements.

Identified key differences from Border's theorem in the context of complementarities.

Applied results to barter and compromise problems involving indivisible objects.

Abstract

We investigate the implementation of reduced-form allocation probabilities in a two-person bargaining problem without side payments, where the agents have to select one alternative from a finite set of social alternatives. We provide a necessary and sufficient condition for the implementability. We find that the implementability condition in bargaining has some new feature compared to Border's theorem. Our results have applications in compromise problems and package exchange problems where the agents barter indivisible objects and the agents value the objects as complements.