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Theory of BAR games

By Allen Clement, Edmund Wong, Harry Li, Lorenzo Alvisi and Mike Dahlin


Distributed systems that span multiple administrative domains require protocols that tolerate both Byzantine and selfish nodes. This paper offers a theory that can be used to analyze such protocols. The theory systematically extends traditional game theory solution concepts through an ex ante analysis that incorporates a rational player’s awareness of the possible presence of Byzantine players in the player’s utility function. We illustrate our approach by modeling synchronous Terminating Reliable Broadcast as a game. We show that Dolev and Strong’s Byzantine TRB protocol with message authentication is not a Nash equilibrium and that rational deviations from it may lead to violation of the TRB safety properties. We present a new TRB protocol with the same asymptotic complexity of Dolev-Strong and prove it to be a Nash equilibrium. Finally, we prove that (k-t) robustness, a recently proposed solution concept for games with Byzantine and rational players, cannot yield an equilibrium in games, such as our TRB game, that model systems where any node may crash and communication is necessary and incurs cost.

Year: 2007
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