On the Shapley value of liability games

Péter Csóka, Ferenc Illés and Tamás Solymosi

European Journal of Operational Research, 2022, vol. 300, issue 1, 378-386

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.

Keywords: Game theory; Shapley value; Constant-sum game; Liability game; Insolvency (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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Working Paper: On the Shapley value of liability games (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:300:y:2022:i:1:p:378-386

DOI: 10.1016/j.ejor.2021.10.012

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