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We study the incentives behind double-spend attacks on Nakamoto-styleProof-of-Work cryptocurrencies. In these systems, miners are allowed to choosewhich transactions to reference with their block, and a common strategy forselecting transactions is to simply choose those with the highest fees. Thiscan be problematic if these transactions originate from an adversary withsubstantial (but less than 50\%) computational power, as high-valuetransactions can present an incentive for a rational adversary to attempt adouble-spend attack if they expect to profit. The most common mechanism fordeterring double-spend attacks is for the recipients of large transactions towait for additional block confirmations (i.e., to increase the attack cost). Weargue that this defense mechanism is not satisfactory, as the security of thesystem is contingent on the actions of its users. Instead, we propose thatdefending against double-spend attacks should be the responsibility of theminers; specifically, miners should limit the amount of transaction value theyinclude in a block (i.e., reduce the attack reward). To this end, we modelcryptocurrency mining as a mean-field game in which we augment the standardmining reward function to simulate the presence of a rational, double-spendingadversary. We design and implement an algorithm which characterizes thebehavior of miners at equilibrium, and we show that miners who use theadversary-aware reward function accumulate more wealth than those who do not.We show that the optimal strategy for honest miners is to limit the amount ofvalue transferred by each block such that the adversary's expected profit is 0.Additionally, we examine Bitcoin's resilience to double-spend attacks. Assuminga 6 block confirmation time, we find that an attacker with at least 25% of thenetwork mining power can expect to profit from a double-spend attack.

Majority is Not Required: A Rational Analysis of the Private Double-Spend Attack from a Sub-Majority Adversary