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Bank Runs: The Predeposit Game

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  • Shell, Karl
  • Zhang, Yu

Abstract

We analyze in some detail the full predeposit game in a simple, tractable, yet very rich, banking environment. How does run-risk affect the optimal deposit contract? If there is a run equilibrium in the postdeposit game, then the optimal contract in the predeposit game tolerates small-probability runs. However, this does not mean that small changes in run-risk are ignored. In some cases, the optimal contract becomes—as one would expect—strictly more conservative as the run-probability increases (until it switches to the best run-proof contract), and the equilibrium allocation is not a mere randomization over the equilibrium allocations from the postdeposit game. In other cases, the allocation is a mere randomization over the equilibria from the postdeposit game. In the first cases (the more intuitive cases), the incentive constraint does not bind. In the second cases, the incentive constraint does bind.

Suggested Citation

  • Shell, Karl & Zhang, Yu, 2020. "Bank Runs: The Predeposit Game," Macroeconomic Dynamics, Cambridge University Press, vol. 24(2), pages 403-420, March.
    • Handle: RePEc:cup:macdyn:v:24:y:2020:i:2:p:403-420_6
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    Cited by:

    1. Sim, Khai Zhi, 2024. "Bank bailouts: Moral hazard and commitment," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    2. Sim, Khai Zhi, 2022. "The optimal bailout policy in an interbank network," Economics Letters, Elsevier, vol. 216(C).
    3. Sim, Khai Zhi, 2023. "Monetary and fiscal coordination in preventing bank failures and financial contagion," Journal of Macroeconomics, Elsevier, vol. 75(C).
    4. Huang, Xuesong, 2024. "Sophisticated banking contracts and fragility when withdrawal information is public," Theoretical Economics, Econometric Society, vol. 19(1), January.
    5. Voellmy, Lukas, 2024. "Preventing runs under sequential revelation of liquidity needs," Journal of Economic Dynamics and Control, Elsevier, vol. 158(C).

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