New axiomatizations of the Owen value

Xun-Feng Hu ()
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Xun-Feng Hu: Guangzhou University

Mathematical Methods of Operations Research, 2021, vol. 93, issue 3, No 6, 585-603

Abstract: Abstract In this paper, we propose three new axiomatizations of the Owen value, similar as the axiomatizations of the Shapley value of Chun (Int J Game Theory 20(2):183–190, 1991), van den Brink (Int J Game Theory 30(3):309–319, 2002), and Manuel et al. (Math Methods Oper Res 77:1–14, 2013), respectively. Firstly, we show that the additivity and null player property in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into coalitional strategic equivalence. And then, we prove that the coalitional symmetry (respectively symmetry within union) and additivity in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into a variation of fairness, named as coalitional fairness (respectively fairness within union). Finally, we show that the two fairness axioms in our second axiomatization can be weakened into two axioms, involving a special relation between players, named as indifference. Besides characterizing the Owen value, we also illustrate that our results can be extended to the Winter value, being a common single-valued solution for cooperative games with a level structure.

Keywords: Cooperative game; Coalition structure; Owen value; Shapley value; Winter value; Level structure; 91A06; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 D63 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00186-021-00743-z

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