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Stability in barter exchange markets

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Abstract

The notion of stability is the foundation of several classic problems in economics and computer science that arise in a wide-variety of real-world situations, including Stable Marriage, Stable Roommate, Hospital Resident and Group Activity Selection. We study this notion in the context of barter exchange markets. The input of our problem of interest consists of a set of people offering goods/services, with each person subjectively assigning values to a subset of goods/services offered by other people. The goal is to find a stable transaction, a set of cycles that is stable in the following sense: there does not exist a cycle such that every person participating in that cycle prefers to his current “status”. For example, consider a market where families are seeking vacation rentals and offering their own homes for the same. Each family wishes to acquire a vacation home in exchange of its own home without any monetary exchange. We study such a market by analyzing a stable transaction of houses involving cycles of fixed length. The underlying rationale is that an entire trade/exchange fails if any of the participating agents cancels the agreement; as a result, shorter (trading) cycles are desirable. We show that given a transaction, it can be verified whether or not it is stable in polynomial time, and that the problem of finding a stable transaction is NP-hard even if each person desires only a small number of other goods/services. Having established these results, we study the problem of finding a stable transaction in the framework of parameterized algorithms.

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Notes

  1. Note that for a fixed exchange X, there is exactly one outgoing arc and exactly one incoming arc incident on every vertex in X.

  2. Note that u’s evaluation of v’s property is scalable based on u’s evaluation of the various attributes of v’s property.

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Acknowledgements

We thank anonymous reviewers for their valuable comments and suggestions which helped to improve the paper.

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Authors and Affiliations

  1. National Institute for Science Education and Research, HBNI, Jatni, India

    Sushmita Gupta

  2. Department of Informatics, University of Bergen, Bergen, Norway

    Fahad Panolan

  3. The Institute of Mathematical Sciences, HBNI, Chennai, India

    Saket Saurabh

  4. Ben-Gurion University of the Negev, Beersheba, Israel

    Meirav Zehavi

Authors
  1. Sushmita Gupta
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  2. Fahad Panolan
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  3. Saket Saurabh
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  4. Meirav Zehavi
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Correspondence to Sushmita Gupta.

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F. Panolan: This work is supported by the European Research Council (ERC) via Grant LOPPRE, Reference 819416 and Norwegian Research Council via Project MULTIVAL.

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Gupta, S., Panolan, F., Saurabh, S. et al. Stability in barter exchange markets. Auton Agent Multi-Agent Syst 33, 518–539 (2019). https://doi.org/10.1007/s10458-019-09414-0

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