The CoinAlg Bind: Profitability-Fairness Tradeoffs in Collective Investment Algorithms

TL;DR

The paper investigates a fundamental tension in CoinAlgs, the shared-investment algorithms driving collective trading in crypto and beyond. It formalizes privacy and economic fairness, proving that unfair value extraction requires some information asymmetry (privacy) and that public transparency imposes a cost to profitability via arbitrage, captured through game-theoretic models (ultimatum and Stackelberg-style sandwiching) and empirical Uniswap analyses. The work shows a dual bind: private CoinAlgs enable insider exploitation, while transparent ones become vulnerable to arbitrage and profit erosion; it also demonstrates that even limited information leakage can significantly erode returns. Empirically, they simulate profitable CoinAlgs under leakage and validate that adversarial strategies such as strategy theft and sandwiching degrade profits across a wide parameter space, motivating guardrails like randomization, protected training pipelines, and bug-bounty incentives. Overall, the paper establishes the CoinAlg Bind as an intrinsic tradeoff and calls for principled mechanisms to mitigate value-extraction while preserving the benefits of shared investment tooling in DeFi and beyond.

Abstract

Collective Investment Algorithms (CoinAlgs) are increasingly popular systems that deploy shared trading strategies for investor communities. Their goal is to democratize sophisticated -- often AI-based -- investing tools. We identify and demonstrate a fundamental profitability-fairness tradeoff in CoinAlgs that we call the CoinAlg Bind: CoinAlgs cannot ensure economic fairness without losing profit to arbitrage. We present a formal model of CoinAlgs, with definitions of privacy (incomplete algorithm disclosure) and economic fairness (value extraction by an adversarial insider). We prove two complementary results that together demonstrate the CoinAlg Bind. First, privacy in a CoinAlg is a precondition for insider attacks on economic fairness. Conversely, in a game-theoretic model, lack of privacy, i.e., transparency, enables arbitrageurs to erode the profitability of a CoinAlg. Using data from Uniswap, a decentralized exchange, we empirically study both sides of the CoinAlg Bind. We quantify the impact of arbitrage against transparent CoinAlgs. We show the risks posed by a private CoinAlg: Even low-bandwidth covert-channel information leakage enables unfair value extraction.

Figures (13)

• Figure 1: Example CoinAlgs and whether user assets and their trading algorithm are consolidated or fragmented.
• Figure 2: Overview of popular robo-advisors, showing their assets under management (AUM), number of individual clients, and whether they are private or transparent. Numbers for AUM and number of clients are as of an August 2024 report by Forbes robo-advisors-stats.
• Figure 3: Overview of AI-powered DAOs, showing their peak market cap (MC), peak assets under management (AUM), whether they are private or transparent, and their major asset holdings.
• Figure 4: Game for the economic fairness definition of CoinAlgs.
• Figure 5: Two-move Stackelberg game ${\textsf{Sdwch}}\xspace$, modeling the interaction between transparent CoinAlg $\mathcal{C}\xspace$, acting as leader, and arbitrageur ${\cal A}$ acting as follower. $\mathcal{C}\xspace$ chooses transaction $\tau_1$, which ${\cal A}$ sandwiches. $\mathcal{C}\xspace$'s payoff $\Pi_{\mathcal{C}\xspace}$ is its marginal portfolio value: predicted USD value of purchased TOK minus USD cost (for $\mathcal{C}\xspace^*$, without sandwiching by ${\cal A}$). ${\cal A}$'s payoff is pure USD profit.

Theorems & Definitions (16)

• Definition 1: Privacy of CoinAlgs
• Definition 2: Economic Fairness of CoinAlgs
• Theorem 1
• Theorem 2
• Definition 3: Cost of transparency
• Remark 1: Trade vs. transaction leakage
• Remark 2: (Weak) transparency assumptions
• Remark 3: Determinism vs. non-determinism
• Theorem 3: $\mathcal{C}\xspace$'s cost of transparency in single-shot Game ${\textsf{Sdwch}}\xspace$ is zero.
• Lemma 1