Aggregate monotonic stable single-valued solutions for cooperative games

Calleja, Pedro; Rafels, Carles; Tijs, S.H.

doi:10.1007/s00182-012-0355-5

Cited by 7 publications

(3 citation statements)

References 16 publications

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“…Monotonicity issues have been extensively studied with respect to cooperative game theory (Calleja et al, 2012), political representation (Balinski and Young, 1982), computer resource allocation (Ghodsi et al, 2011), single-peaked preferences (Sönmez, 1994) and other fair division problems. Extensive reviews of monotonicity axioms can be found in chapters 3, 6 and 7 of (Moulin, 2004) and in chapter 7 of Thomson (2011).…”

Section: Related Workmentioning

confidence: 99%

Monotonicity and competitive equilibrium in cake-cutting

Segal-Halevi

Sziklai

2018

Econ Theory

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We study the monotonicity properties of solutions in the classic problem of fair cake-cutting -dividing a heterogeneous resource among agents with different preferences. Resource-and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share or fewer to share among) or all are worse-off (if there is less to share or more to share among).We formally introduce these concepts to the cake-cutting problem and examine whether they are satisfied by various common division rules. We prove that the Nash-optimal rule, which maximizes the product of utilities, is resourcemonotonic and population-monotonic, in addition to being Pareto-optimal, envyfree and satisfying a strong competitive-equilibrium condition. Moreover, we prove that it is the only rule among a natural family of welfare-maximizing rules that is both proportional and resource-monotonic.

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Section: Related Workmentioning

confidence: 99%

Monotonicity and competitive equilibrium in cake-cutting

Segal-Halevi

Sziklai

2018

Econ Theory

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“…Several properties of a fair solution have been identified in cooperative game theory in the last decades. The most crucial properties are (González-Díaz, García-Jurado & Fiestras-Janeiro, 2010, p. 226;Calleja, Rafels & Tijs, 2012;Mueller, 2018, p. 406-408):…”

Section: Properties Of a Fair Solutionmentioning

confidence: 99%

A reply to Ponte et al (2016) Supply chain collaboration: Some comments on the nucleolus of the beer game

Mueller¹

2018

JIEM

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Abstract:Purpose: The aim of the paper is to pick up the result of a previously published paper in order to deepen the discussion. We analyze the solution against the background of some well-known concepts and we introduce a newer one. In doing so we would like to inspire the further discussion of supply chain collaboration.Design/methodology/approach: Based on game theoretical knowledge we present and compare seven properties of fair profit sharing. Findings:We show that the nucleolus is a core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional fairness criteria. Originality/value:We discuss the very involved procedure of establishing lexicographic orders of excess vectors for games with many players.

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“…For our purposes, we introduce a single-valued solutions similar to the one provided by Calleja et al (2012). Let N ∈ N and (N, v) ∈ Γ.…”

Section: S|mentioning

confidence: 99%

Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results

Calleja

Llerena

2016

Soc Choice Welf

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On the domain of cooperative transferable utility games, we investigate if there are single valued solutions that reconcile rationality, consistency and monotonicity (with respect to the worth of the grand coalition) properties. This paper collects some impossibility results on the combination of core selection with either complement or projected consistency, and core selection, max consistency and monotonicity. By contrast, possibility results show up when combining individual rationality, projected consistency and monotonicity.

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Aggregate monotonic stable single-valued solutions for cooperative games

Cited by 7 publications

References 16 publications

Monotonicity and competitive equilibrium in cake-cutting

Monotonicity and competitive equilibrium in cake-cutting

A reply to Ponte et al (2016) Supply chain collaboration: Some comments on the nucleolus of the beer game

Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results

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