Stackelberg Attacks on Auctions and Blockchain Transaction Fee Mechanisms

Abstract: We study an auction with $m$ identical items in a context where $n$ agents can arbitrarily commit to strategies. In general, such commitments non-trivially change the equilibria by inducing a metagame of choosing which strategies to commit to. In this model, we demonstrate a strategy that an attacker may commit to that ensures they receive one such item for free, while forcing the remaining agents to enter into a lottery for the remaining items (albeit for free). The attack is thus detrimental to the auctioneer who loses most of their revenue. For various types of auctions that are not too congested, we show that the strategy works as long as the agents have valuations that are somewhat concentrated. In this case, all agents will voluntarily cooperate with the attacker to enter into the lottery, because doing so gives them a chance of receiving a free item that would have otherwise cost an amount commensurate with their valuation. The attack is robust to a large constant fraction of the agents being either oblivious to the attack or having exceptionally high valuations (thus reluctant to enter into the lottery). For these agents, the attacker may coerce them into cooperating by promising them a free item rather than entering in to the lottery. We show that the conditions for the attack to work hold with high probability when (1) the auction is not too congested, and (2) the valuations are sampled i.i.d. from either a uniform distribution or a Pareto distribution. The attack works for first-price auctions, second-price auctions and the transaction fee mechanism EIP-1559 used by the Ethereum blockchain.