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BAR Nash equilibrium and application to blockchain design

Author

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  • Gorelkina, Olga
  • Laraki, Rida
  • Reynouard, Maxime

Abstract

This paper presents a novel solution concept, called BAR Nash Equilibrium (BARNE) and applies it to the Verifier's Dilemma, a fundamental problem in the design of blockchain consensus. BARNE extends the Nash Equilibrium (NE) to accommodate interactions among Byzantine, altruistic, and rational agents, known as the BAR setting in the distributed computing literature. We prove the existence of BARNE in a broad class of games and introduce two refinements: global stability and local stability. We demonstrate that in the classical quorum-based blockchain protocol, honestly following the prescribed strategy is not a locally stable BARNE, whereas free-riding is a globally stable BARNE. To address this, we designed a more robust protocol with the same classical guarantees, by incorporating fines and forced errors. Under this new protocol, honesty becomes the unique globally stable BARNE, and free-riding is never a BARNE.

Suggested Citation

  • Gorelkina, Olga & Laraki, Rida & Reynouard, Maxime, 2025. "BAR Nash equilibrium and application to blockchain design," Games and Economic Behavior, Elsevier, vol. 154(C), pages 285-301.
    • Handle: RePEc:eee:gamebe:v:154:y:2025:i:c:p:285-301
    DOI: 10.1016/j.geb.2025.09.008
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