VCG Under Sybil (False-name) Attacks -- a Bayesian Analysis

VCG is a classical combinatorial auction that maximizes social welfare. However, while the standard single-item Vickrey auction is false-name-proof, a major failure of multi-item VCG is its vulnerability to false-name attacks. This occurs already in the natural bare minimum model in which there are two identical items and bidders are single-minded. Previous solutions to this challenge focused on developing alternative mechanisms that compromise social welfare. We re-visit the VCG auction vulnerability and consider the bidder behavior in Bayesian settings. In service of that we introduce a novel notion, termed the granularity threshold, that characterizes VCG Bayesian resilience to false-name attacks as a function of the bidder type distribution. Using this notion we show a large class of cases in which VCG indeed obtains Bayesian resilience for the two-item single-minded setting.Comment: This is an extended version of an article to appear in AAAI-2020. Supporting code for generating the article's figures can be found at https://github.com/yotam-gafni/vcg_bayesian_fn

Optimal Mechanism Design for Agents with DSL Strategies: The Case of Sybil Attacks in Combinatorial Auctions

In robust decision making under uncertainty, a natural choice is to go with safety (aka security) level strategies. However, in many important cases, most notably auctions, there is a large multitude of safety level strategies, thus making the choice unclear. We consider two refined notions: (i) a term we call DSL (distinguishable safety level), and is based on the notion of ``discrimin'', which uses a pairwise comparison of actions while removing trivial equivalencies. This captures the fact that when comparing two actions an agent should not care about payoffs in situations where they lead to identical payoffs. (ii) The well-known Leximin notion from social choice theory, which we apply for robust decision-making. In particular, the leximin is always DSL but not vice-versa. We study the relations of these notions to other robust notions, and illustrate the results of their use in auctions and other settings. Economic design aims to maximize social welfare when facing self-motivated participants. In online environments, such as the Web, participants' incentives take a novel form originating from the lack of clear agent identity -- the ability to create Sybil attacks, i.e., the ability of each participant to act using multiple identities. It is well-known that Sybil attacks are a major obstacle for welfare-maximization. Our main result proves that when DSL attackers face uncertainty over the auction's bids, the celebrated VCG mechanism is welfare-maximizing even under Sybil attacks. Altogether, our work shows a successful fundamental synergy between robustness under uncertainty, economic design, and agents' strategic manipulations in online multi-agent systems.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Greedy Transaction Fee Mechanisms for (Non-)myopic Miners

Decentralized cryptocurrencies are payment systems that rely on aligning the incentives of users and miners to operate correctly and offer a high quality of service to users. Recent literature studies the mechanism design problem of the auction serving as a cryptocurrency's transaction fee mechanism (TFM). We present a general framework that captures both myopic and non-myopic settings, as well as different possible strategic models for users. Within this general framework, when restricted to the myopic case, we show that while the mechanism that requires a user to "pay-as-bid", and greedily chooses among available transactions based on their fees, is not dominant strategy incentive-compatible for users, it has a Bayesian-Nash equilibrium where bids are slightly shaded. Relaxing this incentive compatibility requirement circumvents the impossibility results proven by previous works, and allows for an approximately revenue and welfare optimal, myopic miner incentive-compatible (MMIC), and off-chain-agreement (OCA)-proof mechanism. We prove these guarantees using different benchmarks, and show that the pay-as-bid greedy auction is the revenue optimal Bayesian incentive-compatible, MMIC and 1-OCA-proof mechanism among a large class of mechanisms. We move beyond the myopic setting explored in the literature, to one where users offer transaction fees for their transaction to be accepted, as well as report their urgency level by specifying the time to live of the transaction, after which it expires. We analyze pay-as-bid mechanisms in this setting, and show the competitive ratio guarantees provided by the greedy allocation rule. We then present a better-performing non-myopic rule, and analyze its competitive ratio. The above analysis is stated in terms of a cryptocurrency TFM, but applies to other settings, such as cloud computing and decentralized "gig" economy, as well.Comment: 38 pages, 3 figure

Worst-case Bounds on Power vs. Proportion in Weighted Voting Games with Application to False-Name Manipulation

Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs. small players in these games. We model small (big) players as having single (multiple) votes. The aggregate relative power of big players is measured w.r.t. their votes proportion. For this ratio, we show small constant worst-case bounds for the Shapley-Shubik and the Deegan-Packel indices. In sharp contrast, this ratio is unbounded for the Banzhaf index. As an application, we define a false-name strategic normal form game where each big player may split its votes between false identities, and study its various properties. Together, our results provide foundations for the implications of players’ size, modeled as their ability to split, on their relative power.</p

Unified Fair Allocation of Goods and Chores via Copies

We consider fair allocation of indivisible items in a model with goods, chores, and copies, as a unified framework for studying: (1) the existence of EFX and other solution concepts for goods with copies; (2) the existence of EFX and other solution concepts for chores. We establish a tight relation between these issues via two conceptual contributions: First, a refinement of envy-based fairness notions that we term envy without commons (denoted EFX WC when applied to EFX). Second, a formal duality theorem relating the existence of a host of (refined) fair allocation concepts for copies to their existence for chores. We demonstrate the usefulness of our duality result by using it to characterize the existence of EFX for chores through the dual environment, as well as to prove EFX existence in the special case of leveled preferences over the chores. We further study the hierarchy among envy-freeness notions without commons and their α-MMS guarantees, showing, for example, that any EFX WC allocation guarantees at least 11 4 -MMS for goods with copies.</p