Corvinus
Corvinus

On the Shapley value of liability games

Csóka, Péter ORCID: https://orcid.org/0000-0003-1703-5835, Illés, Ferenc and Solymosi, Tamás (2021) On the Shapley value of liability games. European Journal of Operational Research . DOI https://doi.org/10.1016/j.ejor.2021.10.012

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Official URL: https://doi.org/10.1016/j.ejor.2021.10.012

A nyílt hozzáférést az EISZ és a kiadó között létrejött "Read and Publish" szerződés biztosította. Open access was provided "Read and Publish" contract between EIS and the publisher.

Abstract

In a liability problem, the asset value of an insolvent firm must be distributed among the creditors and the firm itself, when the firm has some freedom in negotiating with the creditors. We model the negotiations using cooperative game theory and analyze the Shapley value to resolve such liability problems. We establish three main monotonicity properties of the Shapley value. First, creditors can only benefit from the increase in their claims or of the asset value. Second, the firm can only benefit from the increase of a claim but can end up with more or with less if the asset value increases, depending on the configuration of small and large liabilities. Third, creditors with larger claims benefit more from the increase of the asset value. Even though liability games are constant-sum games and we show that the Shapley value can be calculated directly from a liability problem, we prove that calculating the Shapley payoff to the firm is NP-hard.

Item Type:Article
Uncontrolled Keywords:game theory, shapley value, constant-sum game, liability game, insolvency
Subjects:Mathematics, Econometrics
DOI:https://doi.org/10.1016/j.ejor.2021.10.012
ID Code:6984
Deposited By: Veronika Vitéz
Deposited On:22 Oct 2021 09:06
Last Modified:22 Oct 2021 09:06

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