Cooperative Lot Sizing Games in Supply Chains

Drechsel, Julia

doi:10.1007/978-3-642-13725-9

Cited by 17 publications

(14 citation statements)

References 175 publications

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“…We also provide some error bounds for polyhedral sets applicable to the players' bounding sets X i (t). We later use these results to establish the convergence of the bargaining process in (6).…”

Section: B Preliminary Resultsmentioning

confidence: 95%

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Constrained consensus for bargaining in dynamic coalitional TU games

Nedić

Bauso

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.

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Section: B Preliminary Resultsmentioning

confidence: 95%

“…They have been used to model cooperation in supply chain or inventory management applications [6], [10], network flow applications [2] and in communication networks [20].…”

Section: Introductionmentioning

confidence: 99%

Constrained consensus for bargaining in dynamic coalitional TU games

Nedić

Bauso

2011

IEEE Conference on Decision and Control and European Control Conference

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“…In such games, subadditivity enlightens that players or coalitions have an incentive to form coalitions to lower their costs with respect to the individual costs they would have to aord without cooperating (see [11], Chapter 2, for example).…”

Section: The Atkinson Index As the Characteristic Function Of A Coopementioning

confidence: 99%

A Multi-Factor Inequality Approach to a Transfer Scheme: The Case of Common Agricultural Policy

Палестини

Pignataro

2013

SSRN Journal

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The purpose of this paper is to propose theoretical foundations on the impact of transfer scheme, e.g. Community Agricultural Policy, on income inequality within European Countries. First, we show that ex-post inequality (in the after-transfer distribution) may increase if either initial aggregate income or the amount of scal contributions are suciently high. Second according to welfare ordering, we characterize a multi-factor decomposition of the Atkinson index to gauge the impact of each income source on the inequality prole. Third, we introduce a methodology to construct a cooperative game played by dierent income factors (as net incomes and/or incoming transfers) explicitly measuring the cost of inequality across the population in terms of welfare loss. We nally rely on Banzhaf and Shapley values to determine the marginal contributions of each factor to overall inequality.

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“…Under these assumptions, we will study the dynamic bargaining process in (6). We want to provide conditions under which the process converges to an allocation in the core of the robust game.…”

Section: Assumptionmentioning

confidence: 99%

“…Coalitional TU games have been used to model cooperation in supply chain or inventory management applications [6,10], as well as in network flow applications to coordinate flows of goods, materials, or resources between different production/distribution sites [2]. Recently, coalitional games have also sparked much interest in communication networks.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Coalitional TU Games: Distributed Bargaining Among Players' Neighbors

Nedić

Bauso

2013

IEEE Trans. Automat. Contr.

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We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining process to a random allocation that lies in the core of the robust game under some mild conditions on the underlying communication graphs. The second part of the paper addresses the more general case where the robust game may have empty core. In this case, with the dynamic game we associate a dynamic average game by averaging over time the sequence of characteristic functions. Then, we consider an accordingly modified bargaining protocol. Assuming that the sequence of characteristic functions is ergodic and the core of the average game has a nonempty relative interior, we show that the modified bargaining protocol converges with probability 1 to a random allocation that lies in the core of the average game.

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Cooperative Lot Sizing Games in Supply Chains

Cited by 17 publications

References 175 publications

Constrained consensus for bargaining in dynamic coalitional TU games

Constrained consensus for bargaining in dynamic coalitional TU games

A Multi-Factor Inequality Approach to a Transfer Scheme: The Case of Common Agricultural Policy

Dynamic Coalitional TU Games: Distributed Bargaining Among Players' Neighbors

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