We study trade networks with a tree structure, where a seller with a single indivisible good is connected to buyers, each with some value for the good, via a unique path of intermediaries. Agents in the tree make multiplicative revenue share offers to their parent nodes, who choose the best offer and offer part of it to their parent, and so on; the winning path is determined by who finally makes the highest offer to the seller. In this paper, we investigate how these revenue shares might be set via a natural bargaining process between agents on the tree, specifically, egalitarian bargaining between endpoints of each edge in the tree. We investigate the fixed point of this system of bargaining equations and prove various desirable for this solution concept, including (i) existence, (ii) uniqueness, (iii) efficiency, (iv) membership in the core, (v) strict monotonicity, (vi) polynomial-time computability to any given accuracy. Finally, we present numerical evidence that asynchronous dynamics with randomly ordered updates always converges to the fixed point, indicating that the fixed point shares might arise from decentralized bargaining amongst agents on the trade network.

本文通过自然的交易流程，研究了具有树形结构的贸易网络中收益份额如何被设置，并证明了这种解决方案概念具有存在性、唯一性、效率性、核心成员身份、严格单调性和可任意精度的多项式时间可计算性。最后，本文提供了数值证据，随机更新的异步动态始终收敛于固定点，表明固定点份额可能来自于贸易网络上代理商之间的分散谈判。

在树形交易网络上谈判收入份额