Path monotonicity, consistency and axiomatizations of some weighted solutions

Pedro Calleja () and Francesc Llerena ()
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Pedro Calleja: Universitat de Barcelona
Francesc Llerena: Universitat Rovira i Virgili and CREIP
Authors registered in the RePEc Author Service: Francesc Llerena Garrés

International Journal of Game Theory, 2019, vol. 48, issue 1, No 12, 287-310

Abstract: Abstract On the domain of cooperative games with transferable utility, we introduce path monotonicity, a property closely related to fairness (van den Brink, in Int J Game Theory 30:309–319, 2001). The principle of fairness states that if a game changes by adding another game in which two players are symmetric, then their payoffs change by the same amount. Under efficiency, path monotonicity is a relaxation of fairness that guarantees that when the worth of the grand coalition varies, the players’ payoffs change according to some monotone path. In this paper, together with the standard properties of projection consistency (Funaki, in Dual axiomatizations of solutions of cooperative games. Mimeo, New York, 1998) and covariance, we show that path monotonicity characterizes the weighted surplus division solutions. Interestingly, replacing projection consistency by either self consistency (Hart and Mas-Colell, in Econometrica 57:589–614, 1989) or max consistency (Davis and Maschler, in Nav Res Logist Q 12:223–259, 1965) we obtain new axiomatic characterizations of the weighted Shapley values and the prenucleolus, respectively. Finally, by the duality approach we provide a new axiomatization of the weighted egalitarian non-separable contribution solutions using complement consistency (Moulin, in J Econ Theory 36:120–148, 1985).

Keywords: Consistency; Weighted surplus division solutions; Weighted egalitarian non-separable contribution solutions; Weighted Shapley values; Prenucleolus (search for similar items in EconPapers)
JEL-codes: C71 C78 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00182-019-00661-9

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