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Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk


  • Garratt, Rodney

    () (University of California, Santa Barbara)

  • Webber, Lewis

    () (Bank of England)

  • Willison, Matthew

    () (Bank of England)


An individual bank can put the whole banking system at risk if its losses in response to shocks push losses for the system as a whole above a critical threshold. We determine the contribution of banks to this systemic risk using a generalisation of the Shapley value; a concept originating in co-operative game theory. An important feature of this approach is that the order in which banks fail in response to a shock depends on the composition of the banks’ asset portfolios and capital buffers. We show how these factors affect banks’ contributions to systemic risk, and the extent to which these contributions depend on the level of the critical threshold.

Suggested Citation

  • Garratt, Rodney & Webber, Lewis & Willison, Matthew, 2012. "Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk," Bank of England working papers 468, Bank of England.
  • Handle: RePEc:boe:boeewp:0468

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    References listed on IDEAS

    1. Gauthier, Céline & Lehar, Alfred & Souissi, Moez, 2012. "Macroprudential capital requirements and systemic risk," Journal of Financial Intermediation, Elsevier, vol. 21(4), pages 594-618.
    2. repec:bla:joares:v:17:y:1979:i:1:p:295-303 is not listed on IDEAS
    3. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    4. Lewis Webber & Matthew Willison, 2011. "Systemic capital requirements," BIS Papers chapters,in: Bank for International Settlements (ed.), Macroprudential regulation and policy, volume 60, pages 44-50 Bank for International Settlements.
    5. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    6. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
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    Cited by:

    1. Fuad Aleskerov & Irina Andrievskaya & Elena Permjakova, 2014. "Key Borrowers Detected By The Intensities Of Their Short-range Interactions," HSE Working papers WP BRP 33/FE/2014, National Research University Higher School of Economics.

    More about this item


    Shapley value; systemic risk; bank regulation;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G01 - Financial Economics - - General - - - Financial Crises
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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