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January  2018, 5(1): 9-20. doi: 10.3934/jdg.2018002

On the linearity property for allocation problems and bankruptcy problems

Joss Sánchez-Pérez ,

Facultad de Economía -UASLP; San Luis Potosí, México

* Corresponding address: Facultad de Economía, UASLP; Av. Pintores s/n, Col. B. del Estado 78213, San Luis Potosí, México. Tel. +52 (444) 8342510 Ext. 7023

Received  January 2017 Revised  September 2017 Published  January 2018

This work provides an analysis of linear rules for bankruptcy problems and allocation problems from an axiomatic point of view and we extend the study of the additivity property presented in Bergantiños and Méndez-Naya [1] and Bergantiños and Vidal-Puga [2]. We offer a decomposition for the space of allocation problems into direct sum of subspaces that are relevant to the study of linear rules and obtain characterizations of certain classes of rules. Furthermore, for bankruptcy problems we propose an alternative version of the additivity property.

Keywords: Allocation problems, bankruptcy problems, axiomatic rules.
Mathematics Subject Classification: Primary: 91B32; Secondary: 91B02.
Citation: Joss Sánchez-Pérez. On the linearity property for allocation problems and bankruptcy problems. Journal of Dynamics & Games, 2018, 5 (1) : 9-20. doi: 10.3934/jdg.2018002
References:
[1]

G. Bergantiños and L. Méndez-Naya, Additivity in bankruptcy problems and in allocation problems, Spanish Economic Review, 3 (2001), 223-229.   Google Scholar

[2]

G. Bergantiños and J. Vidal-Puga, Additive rules in bankruptcy problems and other related problems, Mathematical Social Sciences, 47 (2004), 87-101.  doi: 10.1016/S0165-4896(03)00079-9.  Google Scholar

[3]

C. Herrero, M. Maschler and A. Villar, Individual rights and collective responsibility: The rights-egalitarian solution, Mathematical Social Sciences, 37 (1999), 59-77.  doi: 10.1016/S0165-4896(98)00017-1.  Google Scholar

[4]

B. O'Neill, A problem of rights artitration from the Talmud, Mathematical Social Sciences, 2 (1982), 345-371.  doi: 10.1016/0165-4896(82)90029-4.  Google Scholar

[5]

W. Thomson, Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey, Mathematical Social Sciences, 45 (2003), 249-297.  doi: 10.1016/S0165-4896(02)00070-7.  Google Scholar

show all references

References:
[1]

G. Bergantiños and L. Méndez-Naya, Additivity in bankruptcy problems and in allocation problems, Spanish Economic Review, 3 (2001), 223-229.   Google Scholar

[2]

G. Bergantiños and J. Vidal-Puga, Additive rules in bankruptcy problems and other related problems, Mathematical Social Sciences, 47 (2004), 87-101.  doi: 10.1016/S0165-4896(03)00079-9.  Google Scholar

[3]

C. Herrero, M. Maschler and A. Villar, Individual rights and collective responsibility: The rights-egalitarian solution, Mathematical Social Sciences, 37 (1999), 59-77.  doi: 10.1016/S0165-4896(98)00017-1.  Google Scholar

[4]

B. O'Neill, A problem of rights artitration from the Talmud, Mathematical Social Sciences, 2 (1982), 345-371.  doi: 10.1016/0165-4896(82)90029-4.  Google Scholar

[5]

W. Thomson, Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey, Mathematical Social Sciences, 45 (2003), 249-297.  doi: 10.1016/S0165-4896(02)00070-7.  Google Scholar

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