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Uniqueness of Clearing Payment Matrices in Financial Networks

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  • Csóka, Péter
  • Herings, P. Jean-Jacques

    (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics)

Abstract

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component which contains more than one agent is called a cycle and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a positive endowment. The division rule used by a cyclical agent with a positive endowment should be positive monotonic and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Since division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. We also show how uniqueness of clearing payment matrices is related to continuity of bankruptcy rules.

Suggested Citation

  • Csóka, Péter & Herings, P. Jean-Jacques, 2021. "Uniqueness of Clearing Payment Matrices in Financial Networks," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2021014
    DOI: 10.26481/umagsb.2021014
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    Cited by:

    1. Csoka, Peter & Herings, P.J.J., 2022. "Centralized Clearing Mechanisms in Financial Networks : A Programming Approach," Discussion Paper 2022-008, Tilburg University, Center for Economic Research.

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    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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