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A constant bound for the periods of parallel chip-firing games with many chips

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Abstract

We prove that any parallel chip-firing game on a graph G with at least 4|E(G)| − |V(G)| chips stabilizes, i.e., such a game has eventual period of length 1. Furthermore, we obtain a polynomial bound on the number of rounds before stabilization. This result is a counterpoint to previous results which showed that the eventual periods of parallel chip-firing games with few chips need not be polynomially bounded.

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Authors and Affiliations

  1. Department of Economics, Massachusetts Institute of Technology, c/o 8520 Burning Tree Road, Bethesda, MD, 20817, USA

    Paul Myer Kominers

  2. Department of Economics, Harvard University, and Harvard Business School, Wyss Hall, Soldiers Field, Boston, MA, 02163, USA

    Scott Duke Kominers

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  1. Paul Myer Kominers
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  2. Scott Duke Kominers
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Correspondence to Scott Duke Kominers.

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The second author gratefully acknowledges the support of a Harvard Mathematics Department Highbridge Fellowship.

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Kominers, P.M., Kominers, S.D. A constant bound for the periods of parallel chip-firing games with many chips. Arch. Math. 95, 9–13 (2010). https://doi.org/10.1007/s00013-010-0129-x

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  • DOI: https://doi.org/10.1007/s00013-010-0129-x

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