Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.15282

Computing Optimal Manipulations in Cryptographic Self-Selection Proof-of-Stake Protocols

Matheus V. X. Ferreira·Aadityan Ganesh·Jack Hourigan·Hannah Huh·S. Matthew Weinberg·Catherine Yu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Cryptographic Self-Selection is a paradigm employed by modern Proof-of-Stake consensus protocols to select a block-proposing "leader." Algorand [Chen and Micali, 2019] proposes a canonical protocol, and Ferreira et al. [2022] establish bounds $f(\alpha,\beta)$ on the maximum fraction of rounds a strategic player can lead as a function of their stake $\alpha$ and a network connectivity parameter $\beta$. While both their lower and upper bounds are non-trivial, there is a substantial gap between them (for example, they establish $f(10\%,1) \in [10.08\%, 21.12\%]$), leaving open the question of how significant of a concern these manipulations are. We develop computational methods to provably nail $f(\alpha,\beta)$ for any desired $(\alpha,\beta)$ up to arbitrary precision, and implement our method on a wide range of parameters (for example, we confirm $f(10\%,1) \in [10.08\%, 10.15\%]$). Methodologically, estimating $f(\alpha,\beta)$ can be phrased as estimating to high precision the value of a Markov Decision Process whose states are countably-long lists of real numbers. Our methodological contributions involve (a) reformulating the question instead as computing to high precision the expected value of a distribution that is a fixed-point of a non-linear sampling operator, and (b) provably bounding the error induced by various truncations and sampling estimations of this distribution (which appears intractable to solve in closed form). One technical challenge, for example, is that natural sampling-based estimates of the mean of our target distribution are \emph{not} unbiased estimators, and therefore our methods necessarily go beyond claiming sufficiently-many samples to be close to the mean.

Explore related subjects

cs.GTcs.CRecon.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Matheus V. X. Ferreira, Aadityan Ganesh, Jack Hourigan, Hannah Huh, S. Matthew Weinberg, Catherine Yu. 2024-06-21. Computing Optimal Manipulations in Cryptographic Self-Selection Proof-of-Stake Protocols. https://doi.org/10.1145/3670865.3673602

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗