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Population monotonic allocation schemes for games with externalities

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  • Takaaki Abe

    (Waseda University)

Abstract

This paper provides conditions for a game with externalities to have a population monotonic allocation scheme (PMAS). We observe that the notion of convexity defined by Hafalir [Games Econ Behav 61:242–258, 2007] does not guarantee the existence of a PMAS in the presence of externalities. We introduce a new notion of convexity and show that while our convexity is not a stronger condition than Hafalir’s [Games Econ Behav 61:242–258, 2007] , it is a sufficient condition for a game to have a PMAS. Moreover, we show that the Aumann-Drèze value, which is defined for games with coalition structures, explicitly constructs a PMAS. In addition, we offer two necessary and sufficient conditions to guarantee a PMAS in the presence of externalities.

Suggested Citation

  • Takaaki Abe, 2020. "Population monotonic allocation schemes for games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 97-117, March.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:1:d:10.1007_s00182-019-00675-3
    DOI: 10.1007/s00182-019-00675-3
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    Cited by:

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    2. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro & A. Jiménez-Losada, 2022. "On convexity in cooperative games with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 265-292, July.

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