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Buck-passing dumping in a garbage-dumping game

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  • Takaaki Abe

    (Tokyo Institute of Technology)

Abstract

We study stable strategy profiles in a pure exchange game of bads, where each player dumps his or her bads such as garbage onto someone else. Hirai et al. (Mathematical Social Sciences 51(2):162–170, 2006) show that cycle dumping, in which each player follows an ordering and dumps his or her bads onto the next player, is a strong Nash equilibrium and that self-disposal is $$\alpha $$ α -stable for some initial distributions of bads. In this paper, we show that a strategy profile of bullying, in which all players dump their bads onto a single player, becomes $$\alpha $$ α -stable for every exchange game of bads. We also provide a necessary and sufficient condition for a strategy profile to be $$\alpha $$ α -stable in an exchange game of bads. In addition, we show that repeating an exchange after the first exchange makes self-disposal stationary.

Suggested Citation

  • Takaaki Abe, 2022. "Buck-passing dumping in a garbage-dumping game," Theory and Decision, Springer, vol. 93(3), pages 509-533, October.
    • Handle: RePEc:kap:theord:v:93:y:2022:i:3:d:10.1007_s11238-021-09858-5
    DOI: 10.1007/s11238-021-09858-5
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    References listed on IDEAS

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    1. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    2. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-684, Part I Se.
    3. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    4. Hirai, Toshiyuki & Masuzawa, Takuya & Nakayama, Mikio, 2006. "Coalition-proof Nash equilibria and cores in a strategic pure exchange game of bads," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 162-170, March.
    5. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, July.
    6. Konishi, Hideo & Quint, Thomas & Wako, Jun, 2001. "On the Shapley-Scarf economy: the case of multiple types of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 1-15, February.
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    Keywords

    Bads; Dumping; Exchange; Stability;
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