This paper addresses the paucity of models of matching markets, both one-sided and two-sided, when utility functions of agents are cardinal. The classical Hylland-Zeckhauser scheme \cite{hylland}, which is the most prominent such model in economics, can be viewed as corresponding to the linear Fisher model, which is most elementary model in market equilibria. Although HZ is based on the attractive idea of using a pricing mechanism, from the viewpoint of use in applications, it has a serious drawback, namely lack of computational efficiency, due to which solving instances of size even 4 or 5 is difficult. We propose a variety of Nash-bargaining-based models, several of which draw from general equilibrium theory, which has defined a rich collection of market models that generalize the linear Fisher model in order to address more specialized and realistic situations. The Nash bargaining solution satisfies Pareto optimality and symmetry and the allocations it yields are remarkably fair. Furthermore, since the solution is captured via a convex program, it is polynomial time computable. In order to be used in "industrial grade" applications, we give implementations for these models that are extremely time efficient, solving large instances, with $n = 2000$, in one hour on a PC, even for a two-sided matching market. The idea underlying our work has its origins in Vazirani (2012), which viewed the linear case of the Arrow-Debreu market model as a Nash bargaining game and gave a combinatorial, polynomial time algorithm for finding allocations via this solution concept, rather than the usual approach of using a pricing mechanism.
翻译:本文论述的是,当代理商的效用功能至关重要时,单面和双面的匹配市场模式缺乏。古典的Hylland-Zeckhauser-Zeckhauser 计划(cite{hylland})是经济学中最突出的这种模式,可被视为与线性Fisher模式相对的,这是市场平衡中最基本的模式。虽然HZ是基于从应用中使用定价机制这一有吸引力的想法,但它有一个严重的缺陷,即缺乏计算效率,因此难以解决4到5个规模的计算效率。我们提出了各种基于Nash-harbalgaus 的模型,其中几个模型来自一般均衡理论,确定了大量市场模型集,将线性Fishercher模式普遍化,以解决更专门和现实的情况。虽然Nash讨价解决方案满足了Pareto最佳性和对称性及其分配的吸引力,但从应用的角度看,它是一个相当公平的模型。由于计算方法是计算方法,因此它具有多面性的时间可调。为了在“工业级-成本”规则中,在2000年采用一个大的时间模型,我们用一个时候的直线性方法,在“工业级的Silal-alalalalalalal-al-al-al-hi在2000年的一个案例上,我们用一个时候使用一个过程进行一个过程中用一个非常的模型,我们用一个非常高的计算。