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A note: characterizations of convex games by means of population monotonic allocation schemes

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Abstract

Convex cooperative games were first introduced by Shapley (Int J Game Theory 1:11–26, 1971) while population monotonic allocation schemes (PMAS) were subsequently proposed by Sprumont (Games Econ Behav 2:378–394, 1990). In this paper we provide several characterizations of convex games and introduce three new notions: PMAS-extendability, PMAS-exactness, and population monotonic set schemes, which imitate the classical concepts that they extend. We show that all of these notions provide new characterizations of the convexity of the game.

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Acknowledgments

We thank J. M. Izquierdo, J. Martínez de Albéniz and M. Núñez for their valuable comments. Institutional support from the Ministerio de Ciencia e Innovación and FEDER under grant ECO2011-22765, and from the Generalitat de Catalunya under grant 2009SGR0960 is acknowledged.

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Authors and Affiliations

  1. Department of Economic, Financial and Actuarial Mathematic, University of Barcelona, Av Diagonal 690, 08034 , Barcelona, Spain

    Jesús Getán, Jesús Montes & Carles Rafels

  2. Department of Economics and Business Sciences, University Abat Oliba CEU, C/ Bellesguard 30, 08022 , Barcelona, Spain

    Jesús Montes

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  1. Jesús Getán
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  2. Jesús Montes
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  3. Carles Rafels
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Correspondence to Jesús Getán.

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Getán, J., Montes, J. & Rafels, C. A note: characterizations of convex games by means of population monotonic allocation schemes. Int J Game Theory 43, 871–879 (2014). https://doi.org/10.1007/s00182-013-0408-4

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  • DOI: https://doi.org/10.1007/s00182-013-0408-4

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