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EURO Journal on Computational Optimization

, Volume 6, Issue 4, pp 367–393 | Cite as

Robust bilateral trade with discrete types

  • Kamyar Kargar
  • Halil Ibrahim Bayrak
  • Mustafa Çelebi Pinar
Original Paper
  • 81 Downloads

Abstract

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 \(\phi \)-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.

Keywords

Mechanism design Robustness Ambiguity \(\phi \)-Divergence 

Mathematics Subject Classification

90C05 91B26 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and EURO - The Association of European Operational Research Societies 2018

Authors and Affiliations

  • Kamyar Kargar
    • 1
  • Halil Ibrahim Bayrak
    • 1
  • Mustafa Çelebi Pinar
    • 1
  1. 1.Department of Industrial EngineeringBilkent UniversityAnkaraTurkey

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