The 2-Shapley value for bicooperative games
In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::39ace3df7027b43155f1c10f6cf83d8e |
| Acceso en línea: | https://hdl.handle.net/11441/186295 https://doi.org/10.1007/s10479-026-07245-3 |
| Access Level: | acceso abierto |
| Palabra clave: | Bicooperative game Shapley value Allocation rules Antimatroid |
| Sumario: | In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while the remaining players abstain. To develop this new value, we employ antimatroid theory not as a structural constraint on the games, but as a methodological bridge. Specifically, we demonstrate that any bicooperative coalition structure is isomorphic to a specific antimatroid, which we term the ‘double antimatroid’. Leveraging this mathematical connection, we propose a new Shapley value, provide an axiomatization that preserves its fundamental axioms, and establish its consistency with existing solution concepts. Finally, we illustrate our theoretical proposal and the calculation of this value through an example modeling a decision-making process. This work provides a robust mathematical foundation connecting both structures, opening new perspectives for analysis within bicooperative game theory. |
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