PaperlayerView exact revision on arXiv

Source-linked AI summary

Towards a Functional Fee Market for Cryptocurrencies

Soumya Basu, David Easley, Maureen O'Hara, Emin Gün Sirer

arXiv:1901.06830v1cs.CRcs.GT

TL;DR

The current cryptocurrency fee market is unstable, and its first-price incentives encourage strategic bidding. The paper adapts second-price auction ideas; as user counts rise, both users’ strategic gains and miners’ manipulation gains converge to zero.

  • Problem

    The current fee market is unstable, making fees difficult for users to choose and miner fee income difficult to predict.

    Source: §1 · p. 2

  • Method

    The paper adapts second-price auction ideas to a fee protocol that accounts for miners’ ability to manipulate transactions and fees.

    Source: §1 · pp. 3–4

  • Results

    As the number of users increases, users’ gains from strategic bidding and miners’ gains from manipulating included transactions both converge to zero.

    Source: §1 · p. 4

  • Takeaways & Limitations

    The proposed alternative removes the need for complex strategic bidding and offers a more stable, predictable fee market.

    Source: §7 · p. 20

    Actual miner payouts under real users and miners remain unclear, partly because the first-price procedure is non-robust.

    Source: §7 · p. 20

Abstract

from arXiv · show

Blockchain-based cryptocurrencies prioritize transactions based on their fees, creating a unique kind of fee market. Empirically, this market has failed to yield stable equilibria with predictable prices for desired levels of service. We argue that this is due to the absence of a dominant strategy equilibrium in the current fee mechanism. We propose an alternative fee setting mechanism that is inspired by generalized second price auctions. The design of such a mechanism is challenging because miners can use any criteria for including transactions and can manipulate the results of the auction after seeing the proposed fees. Nonetheless, we show that our proposed protocol is free from manipulation as the number of users increases. We further show that, for a large number of users and miners, the gain from manipulation is small for all parties. This results in users proposing fees that represent their true utility and lower variance of revenue for miners. Historical analysis shows that Bitcoin users could have saved $272,528,000 USD in transaction fees while miners could have reduced the variance of fee income by an average factor of 7.4 times.

1 Introduction

Bitcoin fees both prioritize transactions and support miners, but strategic first-price bidding creates unstable fees. The paper adapts second-price ideas for a setting where miners can manipulate the auction.

1 Introduction

  • In June 2018, average daily Bitcoin fees ranged from $0.58 to $6.85, while miners’ total daily transaction fees ranged from $11,300 to $1,348,000.The authors say this unpredictability makes fee decisions difficult for users and long-term profitability planning difficult for miners.Source: §1 · p. 2
  • Bitcoin’s first-price fee auction lacks a dominant-strategy equilibrium, encouraging users to shade bids and contributing to observed fee instability.Users may bid low initially and increase fees only when confirmation takes too long.Source: §1 · p. 3
  • The proposed second-price-based mechanism aims for more stable, predictable fees and a more predictable miner revenue stream.The authors expect it to discourage strategic underbidding and reduce user overpayment from overbidding.Source: §1 · pp. 3, 5
  • The design must account for miners’ ability to choose transactions and create fee-paying transactions after seeing users’ proposed fees.The protocol controls payments and miner rewards but cannot require prices to depend on bids from excluded transactions.Source: §1 · pp. 3–4
  • As user counts increase, users’ gains from strategic bidding and miners’ gains from manipulating included transactions both converge to zero.The user result is shown theoretically and through simulations on real distributions.Source: §1 · p. 4
  • Unlike Lavi, Sattath and Zohar [2017], this work targets social welfare with many miners, accepting a weaker non-manipulation result as user incentives vanish with adoption.Their monopolistic-miner protocol seeks higher fee revenue at a cost to social welfare and can leave positive-fee transactions out despite available block space.Source: §1 · p. 5

2 Auction Theory and Sponsored Search

Auction theory and sponsored-search experience motivate second-price-like alternatives, but Bitcoin’s decentralized setting prevents a direct transfer of standard auction rules. The section contrasts auction properties and explains the commitment and information constraints that make Bitcoin different.

2 Auction Theory and Sponsored Search

  • Overture’s generalized first-price sponsored-search auction saw bids rise as excluded advertisers tried again, then crash when prices discouraged bidding.The passage reports that discouraged buyers eventually quit and that the auction produced less revenue than should be possible.Source: §2 · p. 6
  • Sponsored-search experience motivates second-price-like mechanisms: Google’s GSP is simple and works reasonably well, while VCG provides a multi-item second-price generalization with dominant strategies.The paper’s generalized second-price auction for identical items is not Google’s GSP procedure.Source: §2 · pp. 6–7
  • The protocol’s objectives are socially optimal slot assignment, incentives for non-strategic behavior, and simple, obvious strategies for users and miners.Social optimality means assigning slots to the highest-value users and excluding a user only when no lower-value included user exists.Source: §2 · pp. 6–7
  • A generalized second-price auction sells K items to the K highest bidders at the K + 1st highest bid; under the stated standard assumptions, truthful bidding is weakly dominant and assignment is efficient.The auctioneer must be able to commit to the auction form, and bidders’ values are assumed to be iid draws from a fixed distribution.Source: §2 · pp. 7–8
  • Generalized first-price auctions can also yield efficient assignments in equilibrium, but efficiency depends on bidders finding strategies that best respond to one another.In the single-item example, the first-price strategy depends on the number of bidders, the uniform value distribution, and others using the same strategy.Source: §2 · p. 8
  • Bitcoin cannot directly implement the standard generalized second-price auction because miners cannot commit, the K + 1st bid is unobservable, and miners can insert fake bids after observing fees.A miner’s fictitious transactions can turn a nominal second-price auction into a first-price outcome; the analysis considers the blockchain game one block at a time while accounting for waiting time indirectly.Source: §2 · pp. 9–10

3 Model

The model treats block space as K transaction slots and compares the current fee game with a generalized second-price alternative. It shows that the current model has an efficient symmetric equilibrium, while the direct second-price design loses truth-telling incentives when miners can manipulate it.

3 Model

  • In the model, users have one transaction each, values are iid, and active users submit bids without knowing others’ values or bids; miners choose transactions after seeing bids.The analysis considers blocks with more active users than slots and treats transactions as occupying the same amount of space.Source: §3 · p. 11
  • The current protocol is a generalized first-price auction: the K highest bids win and each winner pays their own bid; its symmetric Bayes-Nash equilibrium is efficient.In that equilibrium, the highest-value transactions are placed on the block.Source: §3 · pp. 11–12
  • If miners could commit and the protocol could use all bids, a generalized second-price auction would make truthful bidding weakly dominant and assignments efficient.The payment would be the K + 1st highest bid.Source: §3 · p. 12
  • The efficiency result is limited to symmetric user distributions and one transaction per user; asymmetric distributions or users seeking multiple slots can break it.The paper notes that equilibria need not be symmetric under asymmetric distributions.Source: §3 · p. 12
  • That second-price design is infeasible under miner manipulation: with K = 2, a miner can insert fake bids that improve its fee revenue, except when at least K + 1 bids share the highest value.For three bids f1 > f2 > f3, the described manipulations yield total fees of 2f2 or f1, with the latter better when f1/2 > f2.Source: §3 · p. 13

4 Proposed Mechanism

The protocol adapts a generalized second-price auction while addressing miners’ ability to choose block contents and manipulate bids. It combines a fill requirement and averaged miner rewards with limits on strategic gains as user numbers grow.

4 Proposed Mechanism

  • The protocol addresses miners’ inability to use the K + 1st bid and their incentive to manipulate, while making outcomes independent of which identities they mine under.The design is intended to apply uniformly even when miners create identities they control.Source: §4 · p. 13
  • Included transactions pay the minimum fee among those included, while only K transactions are priced by the auction and other included transactions pay no fee.The miner can fill the block to capacity, but the auction applies to only K transactions.Source: §4 · pp. 13–14
  • A miner is paid the average fee revenue across the most recent B blocks, including the current block, only if the block is filled.A block is filled when it contains K transactions or the miner pays a fill penalty; K may be set as a fraction of block capacity.Source: §4 · p. 14
  • The fill penalty is intended to deter manipulation because it makes fake transactions costly, while the miner recovers only a fraction of those fees in expectation.Larger blocks also face a higher chance of being forked, and the choice of B is blockchain-specific.Source: §4 · p. 15
  • When indifferent, miners are assumed to favor the K highest-value transactions because they have an incentive to support the cryptocurrency’s success.The assumption matters because transactions above the minimum fee do not otherwise affect miner revenue when the miner is not party to them.Source: §4 · p. 15
  • Truthful bidding is not dominant, but when others bid truthfully a user’s expected gain from strategic bidding converges to zero as the number of users grows.For uniform values on [0, 1], the gain bound is 1/A for A active users.Source: §4 · p. 16

5 Large Number of Users

The analysis considers a simpler variant that pays a miner the block’s own revenue and characterizes when manipulation is unattractive. It also shows asymptotic efficiency for both generalized auction forms.

5 Large Number of Users

  • Under the modified rule paying a block miner its block’s revenue, a miner can manipulate via a fictitious transaction; avoiding manipulation requires KfK to exceed nfn for every smaller n, while sequential inequalities suffice.The sequential conditions nfn > (n −1)fn−1 are sufficient, not asserted to be equivalent to the full condition.Source: §5 · pp. 16–17
  • Under the simpler current-block-revenue payment, miners’ manipulation gain vanishes as active users grow when the stated inequalities hold.The inequalities are satisfied asymptotically under truthful bids because the fee terms approach the mean value while adjacent-fee differences approach zero.Source: §5 · pp. 16–17
  • With many users, both generalized first-price and uniform-price generalized second-price auctions have realized social surplus and miner revenue ratios that converge almost surely to their maxima.The result applies to any Bayes-Nash equilibrium of either auction.Source: §5 · p. 17
  • For sufficiently many users, both miners and users have little incentive to manipulate the uniform-price auction using the Kth-highest fee.Source: §5 · p. 17

6 Analysis

The analysis tests miner manipulation by simulation and estimates user savings and miner payout variability from historical bids. Its findings support low manipulation gains under reasonable simulation parameters and lower fees and payout variance under the proposed mechanism.

6 Analysis

  • The analysis uses real-distribution simulations to assess miner manipulation, historical Bitcoin and Ethereum bids to estimate user overpayment, and those bids to estimate miner revenue variance.Source: §6 · p. 17

6.1 Miner Manipulation

  • The simulations draw bids from a power law distribution with a 2-cent median and 10-cent mean, then compare honest inclusion of K transactions with manipulation using fake transactions.The bid distribution is described as similar to Bitcoin’s July 2018 transaction-fee distribution.Source: §6.1 · p. 18
  • Simulated manipulation gains decline as the number of miners or the number of averaged blocks increases, with lower gains at high miner counts.The stated mechanism is that more miners reduce an individual miner’s chance of winning a block, while averaging spreads expected gains across blocks and manipulation costs remain fixed.Source: §6.1 · p. 18
  • Simulations support that optimal miner manipulation does not pay for reasonable parameters, with gains small relative to miner revenue of $15 to $40.The conclusion does not include miners’ incentive to support Bitcoin’s success and their holdings’ value.Source: §6.1 · pp. 18–19

6.2 Blockchain Bid Analysis

  • In Bitcoin, second-price fees have lower variance by up to a factor of 20 on some days, and averaging payouts over B blocks further reduces variance by a factor of B^2.The reported comparisons assume each block’s payment goes to one miner before the additional averaging effect.Source: §6.2 · pp. 19–20
  • Bitcoin and Ethereum bid analyses indicate that the proposed protocol avoids user social waste and decreases miner payout variability, especially during high demand.Bitcoin’s current first-price mechanism is compared with fees recalculated under the proposal.Source: §6.2 · pp. 19–20

7 Conclusion

The conclusion argues that first-price fee mechanisms impose strategic complexity, while a second-price alternative offers a more stable and predictable fee market. The analysis is scoped to proof-of-work protocols, and actual miner payouts under real play remain uncertain.

7 Conclusion

  • The proposed alternative aims to reduce strategic bidding and provide a more stable, predictable fee market for cryptocurrencies.The paper links avoiding cognitive load and complex bidding behavior with cryptocurrencies’ ability to go mainstream.Source: §7 · p. 20
  • With many users relative to block capacity, second-price fees are more robust to strategic bidding than first-price fees, even if equilibrium surpluses are similar.Under second price, a user’s fee affects payment only when the user has the unique Kth-highest bid; under first price, every successful user pays their own bid.Source: §7 · p. 20
  • Second-price procedures empirically yield lower variance in miner fee payouts, but the actual payout with real users and miners remains unclear.In equilibrium, the two procedures are expected to produce approximately the same revenue; the uncertainty is attributed partly to first-price non-robustness.Source: §7 · p. 20
  • The analysis applies to proof-of-work protocols, while cryptocurrencies using other protocols still need some way to prioritize transactions.The paper notes that many cryptocurrencies charge fees and induce a first-price auction, facing the described problems.Source: §7 · pp. 20–21

8 Appendix

The appendix invokes established auction results and gives direct arguments for truthful bidding and bounds on strategic gains. It also identifies standard results used for equilibrium and efficiency claims.

8 Appendix

  • The appendix treats the existence of a symmetric Bayes-Nash equilibrium with increasing bids in a discriminatory multi-unit first-price auction as a standard result [Weber 1983; Milgrom 1985].The text says this is equivalent to Result 1.Source: §8 · p. 21
  • The modified auction is a multi-unit second-price auction with weakly dominant strategies and an efficient equilibrium, cited as a standard result [Weber 1983; Milgrom 1985].Source: §8 · p. 21
  • In the second-price proof, bidding above value can only change the outcome by winning at a price above value, reducing payoff.The bid affects whether the bidder wins, not the conditional price paid.Source: §8 · p. 21
  • Bidding below value can forfeit a slot that would have been won at a price below value, reducing payoff.This case occurs when the bidder’s value exceeds the Kth-highest competing bid, which in turn exceeds the lower bid.Source: §8 · p. 21
  • A user’s maximum strategic gain is bounded by the gap between the K−1st and Kth highest competing bids, whose expected value converges to zero as users increase.The bound applies when the user’s value is at least the Kth-highest competing bid; Result 4 is attributed to Swinkels [2001] and Jackson and Kremer [2006].Source: §8 · pp. 21–22

Figure 1

Figure 1 illustrates sawtooth bid behavior in Overture’s first-price auction for search-ad placements.

Figure 1

  • The figure illustrates sawtooth bids in Overture’s first-price auction for ads shown in response to search queries.It is reproduced from Edelman and Ostrovsky [2007].Source: Figure 1 · p. 26

Figure 2

Figure 2 shows that miner manipulation gains decline as miner count rises, provided the reward is averaged over enough blocks.

Figure 2

  • Increasing the number of miners decreases the gain from manipulation when the reward is averaged over enough blocks.The figure’s simulation fixes the mempool at 2,000 and varies the number of blocks over which the reward is spread.Source: Figure 2 · p. 27

Figure 3

Figure 3 shows that a miner’s gain from manipulation declines as more blocks are averaged, provided there are enough miners.

Figure 3

  • The simulation fixes the mempool at 2,000 transactions while varying the number of blocks averaged.Source: Figure 3 · p. 28
  • Averaging over more blocks decreases a miner’s gain from manipulation when there are enough miners.Source: Figure 3 · p. 28
  • The figure’s trend is conditional on there being enough miners.Source: Figure 3 · p. 28

Figure 4

The figures compare estimated user savings under the proposed scheme with current fee mechanisms and show lower fee-payout variance under second-price mechanisms. The comparisons cover Bitcoin and Ethereum in December 2017.

Figure 4

  • Figure 4 shows substantial daily Bitcoin user savings under the proposed scheme relative to the generalized first-price auction.Source: Figure 4 · p. 29

Figure 5

  • Figure 5 shows lower user savings for Ethereum than Bitcoin, consistent with Ethereum’s higher throughput.Source: Figure 5 · p. 30

Figure 6

  • Figure 6 shows significantly higher Bitcoin miner fee-payout variance under the first-price auction than under the second-price mechanism.Source: Figure 6 · p. 31

Figure 7

  • Figure 7 shows significantly higher Ethereum miner fee-payout variance under the first-price auction than under the second-price mechanism.Source: Figure 7 · p. 32
Loading 1901.06830v1…