Consistency and monotonicity in assignment problems

Sasaki, Hiroo

doi:10.1007/bf01243039

Cited by 26 publications

(48 citation statements)

References 20 publications

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“…Afterwards Housman and Clark (1998) extended this result to games with 4 players. Sasaki (1995) and Nunez and Rafels (2002) analyzed monotonicity in assignment games. None of the monotonicity properties studied above, however, covers the cases that we analyze in this paper.…”

Section: Introductionmentioning

confidence: 99%

Stability and monotonicity in newsvendor situations

Özen¹,

Erkip

Slikker

2012

European Journal of Operational Research

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a b s t r a c tThis study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers' dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.

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Section: Introductionmentioning

confidence: 99%

Stability and monotonicity in newsvendor situations

Özen¹,

Erkip

Slikker

2012

European Journal of Operational Research

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“…Eriksson and Karlander (2001) refer to roommate games with transferable utility, Sotomayor (2005) analyzes one-sided assignment games, and Talman and Yang (2008) study partner formation problems. We use the "one-sided" terminology to emphasize the relation of our results with those of Sasaki (1995) for two-sided assignment problems. A one-sided problem consists of a set of agents and a value function that specifies the value each pair of agents creates if matched (single agents do not create any value).…”

Section: Introductionmentioning

confidence: 99%

“…However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is nonempty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problems. …”

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confidence: 99%

Consistency in one-sided assignment problems

Klaus

Nichifor

2010

Soc Choice Welf

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One-sided assignment problems combine important features of two wellknown matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the division of payoffs to agents is flexible as part of the solution. We take a similar approach to one-sided assignment problems as Sasaki (Int J Game Theory 24:373-397, 1995) for two-sided assignment problems, and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [Pareto indifference and consistency] or [invariance with respect to unmatching dummy pairs, continuity, and consistency], then it coincides with the core (Theorems 1 and 2 ). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is nonempty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problems.

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“…However, axiomatic characterizations of solutions in this framework have been mainly focused on the core (Sasaki, 1995;Toda, 2003 and2005).…”

Section: Introductionmentioning

confidence: 99%

An axiomatization of the nucleolus of assignment markets

2014

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On the domain of two-sided assignment markets with agents' reservation values, the nucleolus is axiomatized as the unique solution that satisfies consistency with respect to Owen's reduced game and symmetry of maximum complaints of the two sides. As an adjunt, we obtain a geometric characterization of the nucleolus by means of a strong form of the bisection property that characterizes the intersection between the core and the kernel of a coalitional game in Maschler et al. (1979).

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Consistency and monotonicity in assignment problems

Cited by 26 publications

References 20 publications

Stability and monotonicity in newsvendor situations

Stability and monotonicity in newsvendor situations

Consistency in one-sided assignment problems

An axiomatization of the nucleolus of assignment markets

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