Robust bilateral trade with discrete types

Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC...

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Autores principales:	Kamyar Kargar, HalilIbrahim Bayrak, MustafaÇelebi Pinar
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2018
Materias:	90C05 91B26 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/354eeeda85bf4f6582294ee474515a76
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spelling	oai:doaj.org-article:354eeeda85bf4f6582294ee474515a762021-12-02T05:01:09ZRobust bilateral trade with discrete types2192-440610.1007/s13675-018-0106-xhttps://doaj.org/article/354eeeda85bf4f6582294ee474515a762018-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621001076https://doaj.org/toc/2192-4406Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ-divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.Kamyar KargarHalilIbrahim BayrakMustafaÇelebi PinarElsevierarticle90C0591B26Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 6, Iss 4, Pp 367-393 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C05 91B26 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C05 91B26 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Kamyar Kargar HalilIbrahim Bayrak MustafaÇelebi Pinar Robust bilateral trade with discrete types
description	Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ-divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.
format	article
author	Kamyar Kargar HalilIbrahim Bayrak MustafaÇelebi Pinar
author_facet	Kamyar Kargar HalilIbrahim Bayrak MustafaÇelebi Pinar
author_sort	Kamyar Kargar
title	Robust bilateral trade with discrete types
title_short	Robust bilateral trade with discrete types
title_full	Robust bilateral trade with discrete types
title_fullStr	Robust bilateral trade with discrete types
title_full_unstemmed	Robust bilateral trade with discrete types
title_sort	robust bilateral trade with discrete types
publisher	Elsevier
publishDate	2018
url	https://doaj.org/article/354eeeda85bf4f6582294ee474515a76
work_keys_str_mv	AT kamyarkargar robustbilateraltradewithdiscretetypes AT halilibrahimbayrak robustbilateraltradewithdiscretetypes AT mustafacelebipinar robustbilateraltradewithdiscretetypes
_version_	1718400822041116672

Robust bilateral trade with discrete types

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