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Liability Games

Author

Listed:
  • Csoka, Péter
  • Herings, P. Jean-Jacques

    (Microeconomics & Public Economics, RS: GSBE ETBC)

Abstract

A firm has liabilities towards a group of creditors. We analyze the question of how to distribute the asset value of the firm among the creditors and the firm itself. Compared to standard bankruptcy games as studied in the game theory literature, we introduce the firm as an explicit player and define a new class of transferable utility games called liability games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability game is empty if and only if the firm is insolvent and has multiple positive liabilities. We analyze the nucleolus of the game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity, and liabilities boundedness. We prove that at the nucleolus, the firm gets a strictly higher amount than its stand-alone value if and only if the firm is insolvent and has multiple positive liabilities. The firm is using the threat to pay others to get debt forgiveness and is able to keep a positive amount of its assets. We provide conditions under which the nucleolus coincides with a generalized truncated proportional rule, assigning a non-negative payment to the firm and distributing the remainder in proportion to the liabilities, truncated by the asset value of the firm.

Suggested Citation

  • Csoka, Péter & Herings, P. Jean-Jacques, 2017. "Liability Games," Research Memorandum 031, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2017031
    DOI: 10.26481/umagsb.2017031
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    References listed on IDEAS

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    1. Bezalel Peleg, 1965. "An inductive method for constructing mimmal balanced collections of finite sets," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(2), pages 155-162, June.
    2. W. Max Corden, 1988. "Debt Relief and Adjustment Incentives," IMF Staff Papers, Palgrave Macmillan, vol. 35(4), pages 628-643, December.
    3. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Federico Sturzenegger & Jeromin Zettelmeyer, 2007. "Debt Defaults and Lessons from a Decade of Crises," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262195534, April.
    6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    7. David Benjamin & Mark L. J. Wright, 2009. "Recovery before redemption: A theory of delays in sovereign debt renegotiations," CAMA Working Papers 2009-15, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. William Thomson, 2013. "Game-Theoretic Analysis Of Bankruptcy And Taxation Problems: Recent Advances," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    9. Kornai, J, 1979. "Resource-Constrained versus Demand-Constrained Systems," Econometrica, Econometric Society, vol. 47(4), pages 801-819, July.
    10. Satyajit Chatterjee & Burcu Eyigungor, 2015. "A Seniority Arrangement for Sovereign Debt," American Economic Review, American Economic Association, vol. 105(12), pages 3740-3765, December.
    11. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    12. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
    13. Anderson, Ronald W & Sundaresan, Suresh, 1996. "Design and Valuation of Debt Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 37-68.
    14. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    15. Serkan Arslanalp & Peter Blair Henry, 2005. "Is Debt Relief Efficient?," Journal of Finance, American Finance Association, vol. 60(2), pages 1017-1051, April.
    16. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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