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On the Shapley value of liability games

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  • Csóka, Péter
  • Illés, Ferenc
  • Solymosi, Tamás

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.

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  • Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:1:p:378-386
    DOI: 10.1016/j.ejor.2021.10.012
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    2. Léa Munich, 2023. "Schedule Situations and their Cooperative Game Theoretic Representations," Working Papers 2023-08, CRESE.

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    More about this item

    Keywords

    Game theory; Shapley value; Constant-sum game; Liability game; Insolvency;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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