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Distribution Concepts Under Duplicated Structure

Author

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  • Yu-Hsien Liao

    (Department of Applied Mathematics, National Pingtung University, Pingtung 912301, Taiwan)

Abstract

In the context of standard states, contributors are typically either fully engaged or not engaged at all under interactions with other contributors. However, in real-world situations, contributors may exhibit varying degrees of involvement and operational capacities. Additionally, related influence may differ across various situations. Therefore, this paper introduces distribution concepts utilizing duplicated structures and weights to address these complexities. To examine the mathematical precision and practical applicability of these distribution concepts, we introduce a specific reduction and its analogues, which provide axiomatic characterizations and dynamic processes.

Suggested Citation

  • Yu-Hsien Liao, 2024. "Distribution Concepts Under Duplicated Structure," Mathematics, MDPI, vol. 12(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3609-:d:1524188
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    References listed on IDEAS

    as
    1. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    2. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 679-694, April.
    3. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
    4. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
    5. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
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