On computational complexity of membership test in flow games and linear production games

Fang, Qizhi; Zhu, Shanfeng; Cai, Mao-cheng; Deng, Xiaotie

doi:10.1007/s001820200106

Cited by 30 publications

(18 citation statements)

References 10 publications

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“…Let us finish this section by a final remark concerning a recent result of Fang et al (2002). Their model differs from ours in the sense that capacities are not necessarily 1 and public arcs are not allowed.…”

Section: The Complexitymentioning

confidence: 91%

The nucleolus of balanced simple flow networks

Potters

Reijnierse

Biswas

2006

Games and Economic Behavior

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Section: The Complexitymentioning

confidence: 91%

The nucleolus of balanced simple flow networks

Potters

Reijnierse

Biswas

2006

Games and Economic Behavior

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“…This result fits into the emerging literature that utilizes insights from computational complexity theory in the study of economic-theoretical decision problems. We mention here Gilboa and Zemel (1989); Chu and Halpern (2001); Cechlarova and Hajdukova (2002) ;Fang, Zhu, Cai, and Deng (2002); Woeginger (2003); Baron, Durieu, Haller, and Solal (2004); Baron, Durieu, Haller, Savani, and Solal (2008); Brandt and Fisher (2008); Conitzer and Sandholm (2008); Kalyanaraman and Umans (2008); Procaccia and Rosenschein (2008); Galambos (2009);Hudry (2009) ;Brandt, Fisher, Harrenstein, and Mair (2010); Deb (2011); Apesteguia and Ballester (2010); Talla Nobibon and Spieksma (2010); Cherchye, Demuynck, and De Rock (2011b);? and Demuynck (2013).…”

Section: Introductionmentioning

confidence: 99%

Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms

Nobibon

Cherchye

Crama

et al. 2016

Operations Research

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This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are NP-complete. This makes the application of these tests problematic for (increasingly available) large(r)-scale data sets. We then present two approaches to overcome this negative result. First, we introduce exact algorithms based on mixed-integer programming (MIP) formulations of the collective rationality tests, which can be usefully applied to medium-sized data sets. Next, we propose simulated annealing heuristics, which allow for efficient testing of the collective model in the case of large data sets. We illustrate our methods by a number of computational experiments based on Dutch labor supply data.

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“…In linear production games (Owen, 1975), every solution to the corresponding dual linear program yields an allocation in the core thus core allocations can be found in polynomial time (Schrijver, 1998). Although testing the membership of a given allocation to the core for this class of games is generally co-NP-complete (Fang et al, 2002), in some cases, e.g. flow games on simple networks (Kalai and Zemel, 1982), dual solutions obtain all allocations in the core.…”

Section: Introductionmentioning

confidence: 99%