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International Conference on Algorithmic Decision Theory

ADT 2017: Algorithmic Decision Theory pp 270–283Cite as

Equilibria in Sequential Allocation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10576))

Abstract

Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate that, even for two agents, better responses can cycle. We then present a linear-time algorithm that returns a profile (which we call the “bluff profile”) that is in pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the same as that of the truthful profile and the profile is in pure Nash equilibrium for all cardinal utilities consistent with the ordinal preferences. We show that the outcome of the bluff profile is Pareto optimal with respect to pairwise comparisons. In contrast, we show that an assignment may not be Pareto optimal with respect to pairwise comparisons even if it is a result of a preference profile that is in pure Nash equilibrium for all utilities consistent with ordinal preferences. Finally, we present a dynamic program to compute an optimal Stackelberg strategy for two agents, where the second agent has a constant number of distinct values for the items.

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Notes

  1. 1.

    This argument does not work when the number of other agents is more than one and they have different preferences. It can be shown that for three or more agents, best responses need not result in the same allocation.

  2. 2.

    For readers not familiar with extensive form games and Subgame-Perfect Nash Equilibrium), we refer them to [16].

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Author information

Authors and Affiliations

  1. Data61, CSIRO, Sydney, Australia

    Haris Aziz & Toby Walsh

  2. UNSW, Sydney, Australia

    Haris Aziz & Toby Walsh

  3. University of Oxford, Oxford, UK

    Paul Goldberg

Authors
  1. Haris Aziz
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  2. Paul Goldberg
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  3. Toby Walsh
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Corresponding author

Correspondence to Haris Aziz .

Editor information

Editors and Affiliations

  1. Heinrich Heine University, Düsseldorf, Germany

    Jörg Rothe

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Aziz, H., Goldberg, P., Walsh, T. (2017). Equilibria in Sequential Allocation. In: Rothe, J. (eds) Algorithmic Decision Theory. ADT 2017. Lecture Notes in Computer Science(), vol 10576. Springer, Cham. https://doi.org/10.1007/978-3-319-67504-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-67504-6_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67503-9

  • Online ISBN: 978-3-319-67504-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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