The Dynamics of Cooperative Games

Grotte, Jeffrey H.

doi:10.21236/ad0787579

Cited by 6 publications

(8 citation statements)

References 9 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it also has drawbacks' in particular, it may not be individually rational when the core is empty. While individual rationality may simply be imposed as a constraint (as proposed by Grotte [1970Grotte [ , 1976), another serious difficulty remains. The weak nucleolus may imply payments to dummies' partners who because of, say, geographical isolation, contribute nothing to the cost savings of any coalition.…”

Section: The Least Core and Nucleolusmentioning

confidence: 99%

Cost allocation in water resources development

Young¹,

Okada²,

Hashimoto³

1982

Water Resources Research

244

120

View full text Add to dashboard Cite

Different methods for allocating the joint costs of water supply projects among users are compared on the basis of certain commonsense principles of equity. We contrast the separable costs-remaining benefits (SCRB) method with simple proportional allocation schemes and more sophisticated methods from cooperative game theory, including the Shapley value and variants of the core. Advantages and disadvantages of the methods in practice are examined using a regional water supply system in Sweden. It is argued that these principles provide a useful framework for choosing intelligently among methods. The appropriateness of a method depends on the context, especially on the reliability of information about costs and demands. The conclusion is that there is no one best method, although from a normative standpoint the SCRB method may be one of the worst.

show abstract

Section: The Least Core and Nucleolusmentioning

confidence: 99%

Cost allocation in water resources development

Young¹,

Okada²,

Hashimoto³

1982

Water Resources Research

244

120

View full text Add to dashboard Cite

show abstract

“…30]), viz., Furasov [153,See. 30] constructs effective algorithms for adaptation of a self-adjusting regulator, and Grote [241] proposed for finding Pareto optimal solutions to use as Lyapunov function the payoff functions of the players, defined for each position.…”

Section: Applicationsmentioning

confidence: 99%

Differential games with nonzero sum (cooperative variant)

Tynyanskii¹,

Жуковский²

1981

J Math Sci

View full text Add to dashboard Cite

“…While individual rationality may simply be imposed as a constraint (as proposed in Grotte (1970Grotte ( , 1976), another serious di¢ culty remains. The per-capita prenucleolus may imply payments to dummies ... (a fact …rst noted by Reinhard Selten)".…”

Section: Introductionmentioning

confidence: 99%

Aggregate monotonic stable single-valued solutions for cooperative games

2012

View full text Add to dashboard Cite

We characterize single-valued solutions of transferable utility cooperative games satisfying core selection and aggregate monotonicity. Furthermore, we show that these two properties are compatible with individual rationality, the dummy player property and the symmetry property. We …nish characterizing single-valued solutions satisfying these …ve properties.Resum: En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.JEL classi…cation: C71

show abstract

The Dynamics of Cooperative Games

Abstract: Systems of differential equations are exhibited, the solutions of which converge to optimal points, some of which are shown to coincide with classical solution concepts, to wit, the core, the Shapley ~alue, and, under certain conditions, the Nucleolus.

Cited by 6 publications

References 9 publications

Cost allocation in water resources development

Cost allocation in water resources development

Differential games with nonzero sum (cooperative variant)

Aggregate monotonic stable single-valued solutions for cooperative games

Contact Info

Product

Resources

About