Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution

Besner, Manfred

doi:10.1007/s00182-019-00701-4

Cited by 10 publications

(5 citation statements)

References 18 publications

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“…It states that the payoffs to two players whose contribution to every nonempty coalition not containing 1 The proportional rule is identical to the stand-alone-coalition proportional value in Kamijo and Kongo (2015). 2 For other proportional solutions, we refer to the proportional value (Ortmann 2000;Khmelnitskaya and Driessen 2003;Kamijo and Kongo 2015), the proper Shapley values (Vorob'ev and Liapunov 1998;van den Brink et al 2015), the proportional Shapley value (Béal et al 2018;Besner 2019), and the proportional Harsanyi solution (Besner 2020). 3 We remark that the proportional division value cannot be considered as a weighted division value (Béal et al 2016) or a weighted surplus division value Llerena 2017, 2019) since those values are based on exogenous weights, while the weights in the PD value are determined in the game, specifically they are equal to the stand-alone worths.…”

Section: Introductionmentioning

confidence: 99%

Axiomatizations of the proportional division value

et al. 2021

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We present axiomatic characterizations of the proportional division value for TU-games, which distributes the worth of the grand coalition in proportion to the stand-alone worths of the players. First, a new proportionality principle, called proportional-balanced treatment, is introduced by strengthening Shapley’s symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths. We characterize the family of values satisfying efficiency, weak linearity, and proportional-balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property. Second, we propose appropriate monotonicity axioms, and obtain axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency. Finally, we provide a characterization of proportional standardness.

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Section: Introductionmentioning

confidence: 99%

Axiomatizations of the proportional division value

et al. 2021

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“…When a buyer is accepted in a coalition, a fraction of the seller's tokens is transferred to the buyer according to the token distribution schema from the seller's offer. The tokens > REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) < distribution function 𝑑 𝜈 (𝐶𝑜) for the coalition 𝐶𝑜 is computed using the Harsanyi dividend formula [36]:…”

Section: A Cooperative Games For Self-sufficient Energy Communitiesmentioning

confidence: 99%

“…If the constraints are met the buy order is accepted in the coalition (lines [15][16][17][18][19]. If the prosumer is in a self-sufficient state, flexibility is used to increase its consumption to complete the remaining energy surplus (23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36). The state of the coalition is evaluated using the buy orders that satisfy the constraints stored in the coalition registry.…”

Section: Fig 4 Determine Stable Coalitions By Evaluating the Bids Sub...mentioning

confidence: 99%

Self-sufficient energy communities using cooperative games over blockchain and smart contracts

Toderean¹,

chifu²,

Cioara³

et al. 2023

Preprint

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<p>The small-scale prosumers' decentralized cooperation and aggregation in energy communities are essential to increase renewable energy penetration and to ensure a successful energy transition. Despite their potential small-scale prosumers are not motivated to participate in local energy value chains due to a lack of trust and decentralized cooperation models for capturing local sustainability preferences, most innovation efforts are focused on financial incentives that are anyway very low. In this paper, we propose a solution for prosumers’ decentralized coordination using a cooperative game on top of a blockchain overlay by considering their complementary energy-related features and flexibility for self-sufficient energy communities. We define a governance model based on cooperative games and blockchain-sharing mechanisms reinforce the prosumers' trust to support the decentralized self-organization in coalitions to balance the renewable generation and demand. Self-enforcing smart contracts are used for the blockchain integration of the governance model to allow the decentralized creation and management of prosumers’ coalitions for optimized payoff distribution towards self-sufficiency and using tokens capturing the beyond-financial community level exchanges. The evaluation results show our solution's effectiveness in enabling prosumers to cooperate and create self-sufficient coalitions in a decentralized fashion with low gas consumption and transactional time overhead. </p>

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“…The coalition function v is given by Suppose that the number of essential coalitions is polynomially bounded and we know them and their worths or dividends. Then Remark 6.2 can serve as a blueprint for all TU-values from the Harsanyi set (Vasil'ev, 1978;Vasil'ev and van der Laan, 2002), also called selectope (Hammer et al, 1977;Derks et al, 2000), or for the TU-values from the generalized Harsanyi set (Besner, 2020), for which the coefficients of the related dividends can then be computed in polynomial-time, such as the proportional Shapley value or the proportional Harsanyi solution (Besner, 2020). The representation of the Banzhaf value (Banzhaf, 1965) in van den Brink and van der Laan (1998, Theorem 2.1) is also suitable.…”

Section: General Reflectionsmentioning

confidence: 99%

Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations

Besner

2022

Discrete Applied Mathematics

Self Cite

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Exponential runtimes of algorithms for values for games with transferable utility like the Shapley value are one of the biggest obstacles in the practical application of otherwise axiomatically convincing solution concepts of cooperative game theory. We investigate to what extent the hierarchical structure of a level structure improves runtimes compared to an unstructured player set. Representatively, we examine the Shapley levels value, the nested Shapley levels value, and, as a new value for level structures, the nested Owen levels value. For these values, we provide polynomial-time algorithms (under normal conditions) which are exact and therefore not approximation algorithms. Moreover, we introduce relevant coalition functions where all coalitions that are not relevant for the payoff calculation have a Harsanyi dividend of zero. Our results shed new light on the computation of values of the Harsanyi set as the Shapley value and many values from extensions of this set. KeywordsCooperative game • Polynomial-time algorithm • Level structure • (Nested) Shapley/Owen (levels) value • Harsanyi dividends

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Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution

Cited by 10 publications

References 18 publications

Axiomatizations of the proportional division value

Axiomatizations of the proportional division value

Self-sufficient energy communities using cooperative games over blockchain and smart contracts

Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations

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