Document Open Access Logo

Strategic Payments in Financial Networks

Authors Nils Bertschinger , Martin Hoefer , Daniel Schmand

PDF
Thumbnail PDF

File

LIPIcs.ITCS.2020.46.pdf
  • Filesize: 0.52 MB
  • 16 pages

Document Identifiers

Author Details

Nils Bertschinger
  • Systemic Risk Group, Frankfurt Institute of Advanced Studies, Germany
  • Institute for Computer Science, Goethe University Frankfurt, Germany
Martin Hoefer
  • Institute for Computer Science, Goethe University Frankfurt, Germany
Daniel Schmand
  • Institute for Computer Science, Goethe University Frankfurt, Germany

Acknowledgements

We thank Pascal Lenzner and Steffen Schuldenzucker for valuable discussions and feedback on the results of this paper. NB thanks Dr. h. c. Maucher for funding his position.

Cite As Get BibTex

Nils Bertschinger, Martin Hoefer, and Daniel Schmand. Strategic Payments in Financial Networks. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ITCS.2020.46

Abstract

In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of Ω(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • Nash Equilibrium
  • Financial Network
  • Systemic Risk
  • Price of Anarchy
  • Equilibrium Computation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Daron Acemoglu, Asuman Ozdaglar, and Alireza Tahbaz-Salehi. Systemic Risk in Endogenous Financial Networks. Available at SSRN: https://ssrn.com/abstract=2553900, January 22 2015. Columbia Business School Research Paper No. 15-17.
  2. Nizar Allouch and Maya Jalloul. Strategic Default in Financial Network. Technical report, School of Economics, University of Kent, 2017. Studies in Economics 1721. Google Scholar
  3. Sanjeev Arora, Boaz Barak, Markus Brunnermeier, and Rong Ge. Computational complexity and information asymmetry in financial products. Comm. ACM, 54(5):101-107, 2011. Google Scholar
  4. Yoram Bachrach and Jeffrey Rosenschein. Power in threshold network flow games. Auton. Agents and Multi-Agent Syst., 18(1):106-132, 2009. Google Scholar
  5. Paolo Barucca, Marco Bardoscia, Fabio Caccioli, Marco D'Errico, Gabriele Visentin, Stefano Battiston, and Guido Caldarelli. Network Valuation in Financial Systems, 2016. URL: http://arxiv.org/abs/1606.05164.
  6. Nils Bertschinger, Martin Hoefer, and Daniel Schmand. Strategic Payments in Financial Networks, 2019. URL: http://arxiv.org/abs/1908.01714.
  7. Mark Braverman and Kanika Pasricha. The computational hardness of pricing compound options. In Proc. 5th Symp. Innov. Theoret. Comput. Sci. (ITCS), pages 103-104, 2014. Google Scholar
  8. Rodrigo Cifuentes, Gianluigi Ferrucci, and Hyun Song Shin. Liquidity risk and contagion. Bank of England, Working Paper No. 264, 2005. Google Scholar
  9. Rama Cont and Eric Schaanning. Indirect Contagion and Systemic Stress Testing. Available at SSRN: https://ssrn.com/abstract=2541114, June 13 2017.
  10. Ágnes Cseh and Jannik Matuschke. New and Simple Algorithms for Stable Flow Problems. Algorithmica, 81(6):2557-2591, 2019. Google Scholar
  11. Xiaotie Deng, Toshihide Ibaraki, and Hiroshi Nagamochi. Algorithmic Aspects of the Core of Combinatorial Optimization Games. Math. Oper. Res., 24(3):751-766, 1999. Google Scholar
  12. Pradeep Dubey and Lloyd Shapley. Totally balanced games arising from controlled programming problems. Math. Prog., 29(3):245-267, 1984. Google Scholar
  13. Larry Eisenberg and Thomas Noe. Systemic Risk in Financial Systems. Manag. Sci., 47(2):236-249, 2001. Google Scholar
  14. Maryam Farboodi. Intermediation and Voluntary Exposure to Counterparty Risk. Available at SSRN: https://ssrn.com/abstract=2535900, August 1 2014.
  15. Tom Fischer. No-Arbitrage Pricing under Systemic Risk: Accounting for Cross-Ownership. Math. Finance, 24(1):97-124, 2014. Google Scholar
  16. Tamás Fleiner. On Stable Matchings and Flows. Algorithms, 7(1):1-14, 2014. Google Scholar
  17. Prasanna Gai and Sujit Kapadia. Contagion in financial networks. Proc. Royal Soc. London A: Math. Phys. Eng. Sci., 466(2120):2401-2423, 2010. Google Scholar
  18. Daniel Granot and Frieda Granot. On Some Network Flow Games. Math. Oper. Res., 17(4):792-841, 1992. Google Scholar
  19. Shibashis Guha, Orna Kupferman, and Gal Vardi. Multi-Player Flow Games. In Proc. 17th Conf. Auton. Agents and Multi-Agent Syst. (AAMAS), pages 104-112, 2018. Google Scholar
  20. Brett Hemenway and Sanjeev Khanna. Sensitivity and computational complexity in financial networks. Algorithmic Finance, 5(3-4):95-110, 2016. Google Scholar
  21. Ehud Kalai and Eitan Zemel. Generalized Network Problems Yielding Totally Balanced Games. Oper. Res., 30(5):998-1008, 1982. Google Scholar
  22. Ehud Kalai and Eitan Zemel. Totally Balanced Games and Games of Flow. Math. Oper. Res., 7(3):476-478, 1982. Google Scholar
  23. Orna Kupferman, Gal Vardi, and Moshe Vardi. Flow Games. In Proc. 37th Conf. Found. Software Tech. Theor. Comput. Sci. (FSTTCS), pages 38:1-38:16, 2017. Google Scholar
  24. Evangelos Markakis and Amin Saberi. On the core of the multicommodity flow game. Decis. Support Syst., 39(1):3-10, 2005. Google Scholar
  25. Christos Papadimitriou. Algorithms, Games and the Internet. In Proc. 33rd Symp. Theory Comput. (STOC), pages 749-753, 2001. Google Scholar
  26. L. C. G. Rogers and L. A. M. Veraart. Failure and Rescue in an Interbank Network. Manag. Sci., 59(4):882-898, 2013. Google Scholar
  27. Steffen Schuldenzucker, Sven Seuken, and Stefano Battiston. Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete. In Proc. 8th Symp. Innov. Theoret. Comput. Sci. (ITCS), pages 32:1-32:20, 2017. Google Scholar
  28. Teruyoshi Suzuki. Valuing Corporate Debt: The Effect of Cross-Holdings of Stock and Debt. J. Oper. Res. Soc. Japan, 2, 2002. Google Scholar
  29. Éva Tardos. A strongly polynomial minimum cost circulation algorithm. Combinatorica, 5(3):247-256, 1985. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact