TRAP: The Bait of Rational Players to Solve Byzantine Consensus
About
It is impossible to solve the Byzantine consensus problem in an open network of $n$ participants if only $2n/3$ or less of them are correct. As blockchains need to solve consensus, one might think that blockchains need more than $2n/3$ correct participants. But it is yet unknown whether consensus can be solved when less than $2n/3$ participants are correct and $k$ participants are rational players, which misbehave if they can gain the loot. Trading correct participants for rational players may not seem helpful to solve consensus since rational players can misbehave whereas correct participants, by definition, cannot. In this paper, we show that consensus is actually solvable in this model, even with less than $2n/3$ correct participants. The key idea is a baiting strategy that lets rational players pretend to misbehave in joining a coalition but rewards them to betray this coalition before the loot gets stolen. We propose TRAP, a protocol that builds upon recent advances in the theory of accountability to solve consensus as soon as $n>\max\bigl(\frac{3}{2}k+3t,2(k+t)\bigr)$: by assuming that private keys cannot be forged, this protocol is an equilibrium where no coalition of $k$ rational players can coordinate to increase their expected utility regardless of the arbitrary behavior of up to $t$ Byzantine players. Finally, we show that a baiting strategy is necessary and sufficient to solve this, so-called rational agreement problem. First, we show that it is impossible to solve this rational agreement problem without implementing a baiting strategy. Second, the existence of TRAP demonstrates the sufficiency of the baiting strategy. Our TRAP protocol finds applications in blockchains to prevent players from disagreeing, that could otherwise lead to "double spending".