Epsilon, by Anera Labs Inc

# An Analysis of Competitive Equilibria in Intent- based Bridges ### Vishwa Naik, Konrad Strachan ------ ## Abstract The world of decentralised finance is plagued with complexity. A purported solution to simplifying this complexity has led to the proliferation of "intent" based systems. In these systems, users express their preferences over end state, while delegating the path to accomplishing said end state to a sophisticated third party. The adoption and development in this direction has seen externalities, illuminated by Pai, Chitra, Diamandis and Kulkarni [1]. Lessons from this paper provide us insights on the "oligopoly" in the market on Ethereum L1. We provide a formal analysis of the market structure in Cross-chain "intent" systems. Our investigation into the competitive dynamics among the solvers/fillers/relayers reveals a significant lack of competition, with data from prominent intent-based bridges like Across Protocol V2, DLN and Synapse indicating a concentrated market structure. We show that not only are these markets monopolistic, they are, in fact, solely occupied by the protocol owned. We also point out that the auction design in these systems does not incentive align "best possible execution" for the user and reinforces the priviliged position of the protocol owned relayer. ### Introduction With the proliferation of multiple blockchains and the modular thesis, the need to seamlessly move assets around has never been more pronounced. Arbitrary Message Passing Bridges gave rise to value transfer across multiple chains. Often, the time it takes to settle bridge transactions far exceeds minutes. User demand for speed gave rise to a new architecture, known as Cross-chain "intent" bridges. This architecture involves a new sophisticated intermediary, known as a "solver/filler/relayer" that advances users liquidity optimistically when the user initiates a transaction. These relayers front liquidity and rebalance themselves when the bridge operators settle the balances. In exchange for the uncertainty risk of time and finality, these entities charge a premium to users. Across Protocol and DLN were the first 2 bridges to adopt this architecture, favouring the speed and capital efficiency offered to users. While there have been critiques about this architecture, the benefits for end users i.e speed and no finality risk have seen a considerable volume of order flow in the direction of Intent based bridges. Decentralised, distributed state machines represent the most complex dance of crypoteconomic trade offs. In this paper, we dive into one of those trade offs. We critique the underlying market structure of these Intent based bridges. Specifically, our goal was to understand who these "solvers/fillers/relayers" are and what is the nature of the competitiveness between them. In intent based systems, user preferences on execution are auctioned to "solvers" that generate max surplus for users above their reserve price. On L1, while many entities participate as solvers, centralised market makers seem to have a clear edge. This looks much worse for cross chain. In cross chain systems, "solvers" cannot get around the inventory requirements to participate. To distinguish the roles, we are labelling these cross-chain "solvers" as "relayers". Our data shows us that little to no competition exists between "relayers" today. ## Data Collection - For the purpose of this research paper, we look at the blocks over a 3 month time period. - The table below indicated all of the data collected | Volume | Bids | Prices | Relayers| Users| Timestamps | |--------|------|--------|---------|------|-----| |Absolute volume in $ | Number of bids per transaction | Reserve price expressed by user |Number of relayers| Number of Users | Order creation time, Deposit confirmation time, fill time | Volume of transactions |Number of reverted/failed bids per transaction| Settled price | Associated Relayers| Associated Users| Source chain observable time | ## Metrics 1. We use the HHI and HHI relative to specific ranges to visualise the competition among solvers and the relative competition across different order quantities. 2. We have also calculate the Gini coefficient to further model this inequality and visualize the same using a Lorenz curve. ## Findings Early findings are summarised here https://aneralabs.xyz/dashboard/ Our findings show that a whopping 98.5% of all orders on Across are filled unchallenged, while 91% of the orders on Debrdige are unchallenged. HHI = s₁² + s₂² + ... + sₙ² Where: s₁, s₂, ..., sₙ are the market shares of each firm in the industry. n is the number of firms in the industry. The HHI value ranges from 0 to 10,000 (or 0 to 1 if expressed as a fraction), with higher values indicating greater market concentration and less competition. In our study, transaction data was categorized into logarithmically scaled intervals, reflecting a methodological approach that accommodates the wide distribution of transaction values. This classification strategy ensures that each category captures a meaningful range of data, facilitating a nuanced analysis of transaction patterns. By employing logarithmic scaling, we aim to provide a comprehensive understanding of the data's underlying structure, which is crucial for interpreting the economic dynamics of the dataset under consideration. Using the assigned relayer numbers, the Herfindahl-Hirschman Index (HHI) calculation for the transaction data is as follows: 0-10 Market shares for relayers R₁ to R₉ are: R₁: 1222 / 1863 = 0.6558 R₂: 295 / 1863 = 0.1583 R₃: 97 / 1863 = 0.0520 R₄: 90 / 1863 = 0.0483 R₅: 40 / 1863 = 0.0215 R₆: 18 / 1863 = 0.0097 R₇: 2 / 1863 = 0.0011 R₈: 1 / 1863 = 0.0005 R₉: 1 / 1863 = 0.0005 The HHI is calculated as: HHI = 0.6558² + 0.1583² + 0.0520² + 0.0483² + 0.0215² + 0.0097² + 0.0011² + 0.0005² + 0.0005² = 0.4607 11-50 Market shares for relayers R₁ to R₁₃ are: R₆: 117 / 3263 = 0.0358 R₃: 292 / 3263 = 0.0895 R₂: 550 / 3263 = 0.1686 R₁: 1720 / 3263 = 0.5272 R₁₀: 266 / 3263 = 0.0815 R₄: 140 / 3263 = 0.0429 R₅: 127 / 3263 = 0.0389 R₁₁: 133 / 3263 = 0.0408 R₁₂: 1 / 3263 = 0.0003 R₉: 6 / 3263 = 0.0018 R₁₃: 11 / 3263 = 0.0034 R₇: 1 / 3263 = 0.0003 The HHI is calculated as: HHI = 0.0358² + 0.0895² + 0.1686² + 0.5272² + 0.0815² + 0.0429² + 0.0389² + 0.0408² + 0.0003² + 0.0018² + 0.0034² + 0.0003² = 0.2964 The HHI for these transaction values is 0.2964, or 2964 51-100 Market shares for relayers R₁ to R₁₂ are: R₂: 130 / 1233 = 0.1054 R₆: 84 / 1233 = 0.0681 R₁: 422 / 1233 = 0.3422 R₅: 101 / 1233 = 0.0819 R₁₁: 105 / 1233 = 0.0851 R₄: 66 / 1233 = 0.0535 R₃: 111 / 1233 = 0.0900 R₁₀: 200 / 1233 = 0.1622 R₉: 3 / 1233 = 0.0024 R₁₃: 8 / 1233 = 0.0065 R₇: 2 / 1233 = 0.0016 R₈: 1 / 1233 = 0.0008 The HHI is calculated as: HHI = 0.1054² + 0.0681² + 0.3422² + 0.0819² + 0.0851² + 0.0535² + 0.0900² + 0.1622² + 0.0024² + 0.0065² + 0.0016² + 0.0008² = 0.1755 101-250 Market shares for relayers R₁ to R₁₂ are: R₁: 721 / 2361 = 0.3054 R₃: 288 / 2361 = 0.1219 R₁₁: 170 / 2361 = 0.0720 R₂: 222 / 2361 = 0.0940 R₆: 173 / 2361 = 0.0733 R₁₀: 370 / 2361 = 0.1567 R₄: 114 / 2361 = 0.0483 R₅: 261 / 2361 = 0.1105 R₉: 10 / 2361 = 0.0042 R₁₃: 14 / 2361 = 0.0059 R₇: 7 / 2361 = 0.0030 R₈: 1 / 2361 = 0.0004 The HHI is calculated as: HHI = 0.3054² + 0.1219² + 0.0720² + 0.0940² + 0.0733² + 0.1567² + 0.0483² + 0.1105² + 0.0042² + 0.0059² + 0.0030² + 0.0004² = 0.1915 251-500 Market shares for relayers R₁ to R₁₃ are: R₁: 312 / 1524 = 0.2047 R₂: 126 / 1524 = 0.0827 R₅: 326 / 1524 = 0.2140 R₃: 240 / 1524 = 0.1575 R₆: 147 / 1524 = 0.0964 R₁₀: 239 / 1524 = 0.1568 R₁₁: 115 / 1524 = 0.0755 R₁₂: 1 / 1524 = 0.0007 R₉: 14 / 1524 = 0.0092 R₄: 1 / 1524 = 0.0007 R₁₃: 4 / 1524 = 0.0026 R₈: 2 / 1524 = 0.0013 R₇: 2 / 1524 = 0.0013 The HHI is calculated as: HHI = 0.2047² + 0.0827² + 0.2140² + 0.1575² + 0.0964² + 0.1568² + 0.0755² + 0.0007² + 0.0092² + 0.0007² + 0.0026² + 0.0013² + 0.0013² = 0.1760 501-5000 Market shares for relayers R₁ to R₁₄ are: R₅: 5063 / 8048 = 0.6291 R₃: 306 / 8048 = 0.0380 R₁₀: 1087 / 8048 = 0.1351 R₁: 272 / 8048 = 0.0338 R₆: 464 / 8048 = 0.0577 R₁₁: 486 / 8048 = 0.0604 R₂: 16 / 8048 = 0.0020 R₉: 207 / 8048 = 0.0257 R₁₄: 1 / 8048 = 0.0001 R₈: 83 / 8048 = 0.0103 R₁₂: 1 / 8048 = 0.0001 R₁₃: 23 / 8048 = 0.0029 R₇: 30 / 8048 = 0.0037 The HHI is calculated as: HHI = 0.6291² + 0.0380² + 0.1351² + 0.0338² + 0.0577² + 0.0604² + 0.0020² + 0.0257² + 0.0001² + 0.0103² + 0.0001² + 0.0029² + 0.0037² = 0.4413 5001-25000 Market shares for relayers R₅, R₁₀, R₆, R₉, R₈, and R₇ are: R₅: 1084 / 1507 = 0.7193 R₁₀: 163 / 1507 = 0.1082 R₆: 154 / 1507 = 0.1021 R₉: 77 / 1507 = 0.0511 R₈: 20 / 1507 = 0.0133 R₇: 9 / 1507 = 0.0060 The HHI is calculated as: HHI = 0.7193² + 0.1082² + 0.1021² + 0.0511² + 0.0133² + 0.0060² = 0.5358 25000+ Market shares for relayers R₅, R₉, R₇, and R₈ are: R₅: 436 / 449 = 0.9710 R₉: 9 / 449 = 0.0200 R₇: 3 / 449 = 0.0067 R₈: 1 / 449 = 0.0022 The HHI is calculated as: HHI = 0.9710² + 0.0200² + 0.0067² + 0.0022² = 0.9434 | Transaction Value Range | HHI | Dominant Relayer | Market Share of Dominant Relayer | |-------------------------|--------|------------------|-----------------------------------| | 0-10 | 0.4606 | R1 | 65.58% | | 11-50 | 0.2964 | R1 | 52.72% | | 51-100 | 0.1915 | R1 | 34.22% | | 101-250 | 0.1760 | R5 | 71.93% | | 251-500 | 0.4413 | R5 | 62.91% | | 501-1000 | 0.5358 | R5 | 71.93% | | 1001-2500 | 0.9434 | R5 | 97.10% | The analysis of the Herfindahl-Hirschman Index (HHI) and market share data for various relayers across different transaction value ranges reveals insights into the market structure of this ecosystem. In the lower transaction value range (0-10), the market is moderately concentrated, with a dominant relayer (R1) holding a significant market share. This concentration decreases in the mid-range (11-250), indicating a more competitive environment with a distribution of market share among multiple relayers. However, as the transaction value increases (251-2500), the market structure shifts towards higher concentration, with relayer R5 becoming increasingly dominant, particularly in the highest value range (1001-2500), where it holds an overwhelming majority of the market share. This pattern suggests that while the market is relatively competitive for smaller transactions, it becomes more oligopolistic for larger transactions, with one or two relayers controlling a significant portion of the market. The overall market share data further supports this observation, with R1 and R5 combined covering approximately 49.81% of the transactions across all value ranges. This concentration is indicative of a market structure where a few key players exert considerable influence, especially in higher-value transactions. The HHI for these transaction values is 0.5358, or 5358 when multiplied by 10,000 to express it in the usual HHI scale. | Volume | Across | DLN | Synapse | Squid | |-------------|-------|----------|------------|--------| |x|y| Absolute HHI | Volume | Across | DLN | Synapse | Squid | |-------------|-------|----------|------------|--------| |x|y| HHI Relative to Order Size (Across) | Order Value | 0-10 | 11-50 | 51-100 | 101-250 | 251-500| 501- 5000|5001-25000| 25000 +| |-------------|-------|----------|------------|--------| |HHI | HHI Relative to Order Size (DLN) | Order Value | 0-500 | 500-5000 | 5000-25000 | 25000+ | |-------------|-------|----------|------------|--------| |HHI | R₁: 0x41ee28EE05341E7fdDdc8d433BA66054Cd302cA1 : 1222 R₂: 0x96AE533814f9A128333a2914A631b9Ae690E2B0a : 295 R₃: 0xD45BdA83d11Fda3EdA0107ce9Aa8856b753Fc44e : 97 R₄: 0xbe75079fd259a82054cAAB2CE007cd0c20b177a8 : 90 R₅: 0x428AB2BA90Eba0a4Be7aF34C9Ac451ab061AC010 : 40 R₆: 0x1b59718eaFA2BFFE5318E07c1C3cB2edde354f9C : 18 R₇: 0xb0aac1f129651e62cde6D1AE683c8a49f4d004d1 : 2 R₈: 0xD3C5fADa7563F834D1F5a64ffd9dfC0E00410B2f : 1 R₉: 0xb86d460EDa97e8E4aaC84ed838D9c434F48755fB : 1 DLN 0-10 R₁: 0x555CE236C0220695b68341bc48C68d52210cC35b R₂: 0xeF1eC136931Ab5728B0783FD87D109c9D15D31F1 R₃: 0xAf9Ab5a0632729b50DE150C1B267e5C6542140E6 For the transaction value range of 0-10 (represented as "10"), the market shares are: R₁: 456 / 483 = 0.9441 R₂: 24 / 483 = 0.0497 R₃: 3 / 483 = 0.0062 The HHI is calculated as: HHI = 0.9441² + 0.0497² + 0.0062² = 0.8923 11-50 Using the same relayer labels from the previous calculation: R₁: 648 / 730 = 0.8877 R₂: 69 / 730 = 0.0945 R₄: 11 / 730 = 0.0151 R₅: 2 / 730 = 0.0027 The HHI is calculated as: HHI = 0.8877² + 0.0945² + 0.0151² + 0.0027² = 0.7901 The HHI for this transaction value range is 0.7901, or 7901 when multiplied by 10,000 to express it in the usual HHI scale. 51-100 Using the same relayer labels from the previous calculations: R₁: 432 / 531 = 0.8136 R₂: 78 / 531 = 0.1469 R₄: 16 / 531 = 0.0301 R₆: 5 / 531 = 0.0094 The HHI is calculated as: HHI = 0.8136² + 0.1469² + 0.0301² + 0.0094² = 0.6740 100-250 Using the same relayer labels from the previous calculations: R₁: 788 / 945 = 0.8339 R₂: 127 / 945 = 0.1344 R₄: 23 / 945 = 0.0243 R₆: 5 / 945 = 0.0053 R₇: 2 / 945 = 0.0021 The HHI is calculated as: HHI = 0.8339² + 0.1344² + 0.0243² + 0.0053² + 0.0021² = 0.7106 251-500 Using the same relayer labels from the previous calculations: R₁: 636 / 809 = 0.7864 R₄: 38 / 809 = 0.0470 R₂: 115 / 809 = 0.1421 R₇: 15 / 809 = 0.0185 R₆: 5 / 809 = 0.0062 The HHI is calculated as: HHI = 0.7864² + 0.0470² + 0.1421² + 0.0185² + 0.0062² = 0.6416 501-5000 Using the same relayer labels from the previous calculations: R₁: 1407 / 1789 = 0.7866 R₂: 255 / 1789 = 0.1426 R₄: 107 / 1789 = 0.0598 R₈: 3 / 1789 = 0.0017 R₉: 1 / 1789 = 0.0006 R₁₀: 2 / 1789 = 0.0011 R₁₁: 1 / 1789 = 0.0006 R₆: 13 / 1789 = 0.0073 The HHI is calculated as: HHI = 0.7866² + 0.1426² + 0.0598² + 0.0017² + 0.0006² + 0.0011² + 0.0006² + 0.0073² = 0.6315 5001-25000 Using the same relayer labels from the previous calculations: R₂: 33 / 169 = 0.1953 R₁: 133 / 169 = 0.7870 R₈: 2 / 169 = 0.0118 R₉: 1 / 169 = 0.0059 The HHI is calculated as: HHI = 0.1953² + 0.7870² + 0.0118² + 0.0059² = 0.6538 25000+ Using the same relayer labels from the previous calculations: R₁: 19 / 20 = 0.9500 R₂: 1 / 20 = 0.0500 The HHI is calculated as: HHI = 0.9500² + 0.0500² = 0.9025 Data Collection Period The data for this study was collected over a one-week period, from January 26, 2024, at 13:00 (UTC) to February 2, 2024, at 13:48 (UTC). The analysis encompasses various protocols operating on multiple blockchain networks, including Ethereum L1, Arbitrum, Base, Optimism, Polygon PoS, zkSync Era, Avalanche, BNB Chain, Solana, and Linea. The block numbers corresponding to the start and end of the data collection period for each network are provided in the table below. The protocols analyzed include Across, DLN, Synapse, and Squidv2. The data was extracted from the respective blockchain explorers and aggregated for analysis. | Chain | Protocols | Block Start | Timestamp Start | Block End | Timestamp End | |---------------|-------------------------------|-------------|-----------------|-------------|---------------| | Ethereum L1 | Across, DLN, Synapse, Squidv2 | 19,091,000 | 26/01/24 13:13 | 19,141,000 | 02/02/24 13:27 | | Arbitrum | Across, DLN, Synapse, Squidv2 | 174,380,000 | 26/01/24 13:04 | 176,730,000 | 02/02/24 13:48 | | Base | Across, DLN, Synapse, Squidv2 | 9,742,500 | 26/01/24 13:05 | 10,046,000 | 02/02/24 13:42 | | Optimism | Across, DLN, Synapse, Squidv2 | 115,338,000 | 26/01/24 13:12 | 115,641,300 | 02/02/24 13:42 | | Polygon PoS | Across, DLN, Synapse, Squidv2 | 52,772,500 | 26/01/24 13:13 | 53,038,900 | 02/02/24 13:42 | | zkSync Era | Across | 25,018,500 | 26/01/24 13:13 | 25,594,000 | 02/02/24 13:43 | | Avalanche | DLN, Synapse, Squidv2 | 40,861,000 | 26/01/24 13:17 | 41,156,000 | 02/02/24 13:32 | | BNB Chain | DLN, Synapse, Squidv2 | 35,583,000 | 26/01/24 13:17 | 35,784,800 | 02/02/24 13:45 | | Solana | DLN | 244,233,800 | 26/01/24 13:00 | 245,692,000 | 02/02/24 13:00 | | Linea | DLN, Squidv2 | 1,855,800 | 26/01/24 13:02 | 2,007,335 | 02/02/24 13:44 | ## References 1. Across V2 Relayer Distribution https://dune.com/sandman2797/across-bridge-stats 2. CowSwap Solver Competition https://dune.com/mdank/cowswap-competition https://dune.com/flashbots/cowswap-solver-metrics 3. Private Market Makerm - Solver in Intent/RFQ Systems https://dune.com/flashbots/pmm 4. DLN (Debridge) taker stats (being updated) https://docs.dln.trade/dln-on-chain/quick-start-guide-for-takers 5. Router Protocol "Forwarder" Docs https://docs.routerprotocol.com/tooling/nitro-forwarders 6. Astaria (Intents based NFT Lending) https://x.com/AstariaXYZ/status/1746984402343629055?s=20 7. Latency in Order Flow Auctions https://arxiv.org/pdf/2312.14510.pdf 8. Calculation and comparison of user surplus from ZeroX https://webflow.internal.0x.org/post/a-comprehensive-analysis-on-dex-liquidity-aggregators-performance Wu, F., Thiery, T., Leonardos, S., & Ventre, C. (Year). Strategic Bidding Wars in On-chain Auctions. In the context of a first-come, first-served (FCFS) auction for order flow on a blockchain, the expected payoff function for rational actors can be adjusted to account for the absolute impact of timing errors. In this auction model, the timing of a bid is crucial; any bid submitted after the optimal timestamp has zero chance of winning. Therefore, we define $T_{error}$ as the difference between the actual bid timestamp and the optimal bid timestamp. The expected payoff function is then defined as: \[E[payoff] = \begin{cases} P_{win} \times R - C & \text{if } T_{error} \leq 0 \\ 0 - C & \text{if } T_{error} > 0 \end{cases}\] In this function, $P_{win}$ is the probability of winning the auction if the bid is submitted on time or early, $R$ is the reward for a successful bid, and $C$ is the cost of submitting a bid. If the bid is submitted on time or early ($T_{error} \leq 0$), the expected payoff is calculated as the product of the probability of winning and the reward, minus the cost of bidding. However, if the bid is late ($T_{error} > 0$), the expected payoff drops to the negative cost of bidding, reflecting the zero probability of winning. This model captures the absolute nature of the timing requirement in a FCFS auction, where late bids are categorically disqualified from winning.