Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions
Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions
复制标题
具有离散凹效用函数的多单位交易网络的稳定性和竞争均衡
DOI：
10.1007/s13160-015-0175-7
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发表时间：
2015
影响因子：
0.9
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
Ikebe Y. T;Sekiguchi;Y.;Shioura;A. and Tamura;A.
哈特菲尔德、科米纳斯、尼基福尔、奥斯特洛夫斯基和韦斯特坎普在一个交易网络模型中证明了稳定结果和竞争均衡的存在，假设所有代理人的偏好都满足一个称为完全替代条件的条件。在本文中，我们扩展了他们的模型，使用离散凹效用函数称为扭曲凹函数。我们证明了一个代理商的价值函数是扭曲凹的当且仅当代理商的偏好满足完全替代条件的广义变体。我们还证明了在广义完全替代条件下，扩展模型存在稳定结果和竞争均衡，竞争均衡价格向量集构成一个格。此外，我们讨论了竞争均衡，稳定性和效率之间的联系。最后，我们研究了稳定性，强群稳定性和链稳定性之间的关系，并验证了这三个稳定性概念是等价的，只要所有代理的赋值函数是扭曲凹的。
Hatfield, Kominers, Nichifor, Ostrovsky, and Westkamp showed the existence of stable outcomes and competitive equilibria in a model of trading networks under the assumption that all agents’ preferences satisfy a condition called the full substitutes condition. In this paper, we extend their model by using discrete concave utility functions called twisted-concave functions. We show that a valuation function of an agent is twisted-concave if and only if the agent’s preference satisfies the generalized variant of the full substitutes condition. We also show that under the generalized full substitutes condition, there exist stable outcomes and competitive equilibria in the extended model and the set of competitive equilibrium price vectors forms a lattice. In addition, we discuss the connection among competitive equilibria, stability, and efficiency. Finally, we investigate the relationship among stability, strong group stability, and chain stability and verify these three stability concepts are equivalent as long as valuation functions of all agents are twisted-concave.