Credible, Optimal Auctions via Blockchains

Picture yourself at an auction, surrounded by eager bidders, all hoping to get their hands on the prized possession up for grabs. But as the bidding heats up, you can’t help but question the fairness of the process. Are the bids genuine? Is there any chance of bid manipulation or insider trading?

Holdup a bit. Let’s first understand why we’re at this auction event.

What is an auction?

Fundamentally, an auction is a process of selling and buying goods or services, usually by offering them to the highest bidder.

In traditional auction methods, the credibility and fairness of the process are often questioned due to the possibility of fraudulent activities such as bid manipulation, insider trading, and more. However, the advent of blockchain technology has brought about a new solution to these problems — credible and optimal auctions via blockchains.

Credible auctions

The uncertainty surrounding traditional auctions can be enough to dampen the excitement of participating in one.

…Enter blockchain technology. With its secure, transparent, and decentralized ledger, blockchain has the power to revolutionize the auction world.

This technology makes it possible to conduct auctions in a completely trustless environment, as all participants have equal access to the information and there is no central authority to manipulate the results.

William Vickrey first established the taxonomy of auctions based on the order in which the auctioneer quotes prices and the bidders tender their bids. He established four major (one-sided) auction types:

• The ascending-bid (open, oral, or English) auction;
• The descending-bid (Dutch) auction;
• The first-price, sealed-bid auction; and
• The second-price, sealed-bid (Vickrey) auction.

English auctions start at a reserve price and increase until no one is willing to bid higher, and the winner pays their bid. Dutch auctions start at a high price and decrease until someone calls “Mine!” and wins the item at that price. In both English and Dutch auctions, bidders receive information from other bids.

In a first-price sealed-bid auction, each bidder submits a single bid in a sealed envelope, and the highest bidder wins the item at their bid price. The second-price sealed-bid auction, also known as the Vickrey auction, has bidders submit sealed envelopes and the highest bidder wins the item at the price of the second-highest bidder. This type of auction is rare and is primarily used for setting foreign exchange rates in some African countries.

Now, the use of smart contracts in blockchains has enabled the creation of auction processes that are automated, transparent, and tamper-proof. Remember that a smart contract is a self-executing computer program that automatically executes the terms of an agreement between buyers and sellers once certain conditions are met. In the context of an auction, a smart contract can be programmed to automatically determine the winning bid, distribute payments, and transfer ownership of the goods or services being auctioned. This fact alone has made the Dutch auction the most preferred type of auction among crypto projects.

Now that we have talked about Credible auctions, how do optimal auctions fit into all these?

Optimal auctions

Optimal auctions are those that result in the highest total revenue for the seller and the highest total value for the buyer. There are different types of optimal auctions, such as:

• First-price auctions,
• Second-price auctions, and more.

The type of auction that is chosen depends on the specific requirements and goals of the auction. An optimal auction typically asks the following questions:

1. Who are the participants in the auction and what are their valuations for the item being auctioned?
2. What is the objective of the auction, such as maximizing revenue, fairness, or social welfare?
3. What auction format should be used, such as an English auction, Dutch auction, or Vickrey auction, to achieve the desired objective?
4. How should the auction be designed to prevent strategic bidding, such as collusion or shading of bids?
5. What should be the rules for bidding, such as allowing proxy bidding or restricting bid increments?
6. How should the auction be implemented, such as through a physical auction or a digital platform, and what information should be made available to the participants?

The answers to these questions determine the optimal auction design for a particular scenario. One of the main benefits of using blockchains for auctions is the ability to increase the participation of potential buyers from around the world. This increases the pool of bidders and can result in higher winning bids, as more participants lead to more competition.

Relationship between Optimal auction and Credible auction

An optimal auction is an auction mechanism that maximizes certain objectives, such as the seller’s revenue or the social welfare of the participants. In an optimal auction, bidders truthfully reveal their valuations for the item being auctioned, and the auction mechanism incentivizes them to do so.

A credible auction, on the other hand, is an auction that is believed by the bidders to be fair and impartial, and that the winner will actually receive the item being auctioned. In a credible auction, the bidders have confidence in the auction mechanism and are more likely to participate and make higher bids.

The relationship between optimal auctions and credible auctions is that a credible auction is a necessary condition for an optimal auction to function properly. If an auction is not credible, bidders may be reluctant to participate or may manipulate their bids, leading to suboptimal outcomes. An optimal auction is only truly optimal if it is also credible.

In a paper written by Akbarpour and Li (2020), they defined credibility in auctions as a requirement that the auctioneer not be able to benefit from undetectable deviations from the stated auction process and found that, in a basic model, the ascending price auction with reserves is the only auction that is credible, strategy-proof, and optimizes revenue.

Ferreira and Weinberg (2020) introduced the Deferred Revelation Auction (DRA) as a communication-efficient auction that avoids the limitations found by Akbarpour and Li (2020) under the assumption of the use of cryptographic commitments and as long as bidder valuations are MHR.

ELI5…

The two-stage process starts with bidders posting commitments to their bids along with collateral. In the second stage, they reveal their actual bids, and if they fail to do so, their collateral is forfeited. The central idea behind this process is to ensure that if the auctioneer cheats, for example, by adding a fake bid in a second-price auction, they will be penalized by having their assets seized.

The challenge lies in determining the appropriate amount of collateral required from the bidders. The use of a public blockchain for the posting of commitments limits the ability of the auctioneer to deviate from the rules, as compared to a private setup.

The required collateral for an auction depends on the bidders’ valuations of the item being sold. If the valuation distribution is very spread out, then the collateral required may be significantly higher than the bid amount.

When communication between the auctioneer and bidder occurs through a private channel, it’s challenging to control deviations from honest behaviour due to the large strategy space of deviations. As a result, only “nice” valuation distributions that are not “jumpy” (monotone hazard) can be handled.

However, even when assuming a private channel, some transactions in DEX MEV auctions may require fatter-tailed distributions, and some extreme liquidation cases may not be handled by any independent private auction.

The original credible auction paper suggests modelling the interaction between the bidders and auctioneers as a game tree that includes the set of messages they can exchange. Having commitments on a public blockchain changes the strategy space, allowing for wider and fatter value distributions. This is because by forcing the commitments to be on a public blockchain, the auctioneer cannot deviate as much as in a private setting.

However, Ferreira and Weinberg (2020) showed that DRA is not credible when bidder valuations are strongly regular unless greater than 1. In this paper, the authors inquire about the ability of blockchains to design a wider range of credible auctions. They answer affirmatively by demonstrating that DRA is credible for strongly regular distributions for all values greater than 0 if executed on a secure and censorship-resistant blockchain.

The authors argue that ledger technology offers two properties that reduce deviations from self-interested auctioneers. First, the availability of smart contracts allows for extending credibility to situations where the auctioneer does not have a reputation, addressing one of the main limitations of the definition of credibility from Akbarpour and Li (2020).

Secondly, blockchains enable the implementation of mechanisms through a public broadcast channel, eliminating the adaptive undetectable deviations that led to the negative results of Ferreira and Weinberg (2020).

What does this mean for auctions with Miner Extractable Value (MEV)?

• Networks like Flashbots’ SUAVE and SkipProtocol can serve as a clearinghouse for commitments, which use zero-knowledge proofs, to maintain credibility in auctions.
• Public Broadcast Service (PBS) can be made credible through this auction process if consensus ensures the Deferred Revelation Auction (DRA) and the commitments.

Vitalik Buterin’s concept of “cost to deviate” is relevant to computing the cost of auctioneers deviating and censoring. Other possibilities include using zero-knowledge proofs or Fully Homomorphic Encryption (FHE) to:

• Expand the range of valuation distributions that can be used, particularly in a strict model with FHE.
• Model credible auctions with interdependencies.

And them’s the facts!!!

In a time when even a giant like Google yields to demands for fair auctions, cryptocurrency has the potential to pioneer mechanism design. By using blockchain technology for auctions, it presents a new approach to overcoming the challenges in traditional auction methods. The transparency, security, and decentralized nature of blockchain provide a reliable and efficient auction process that can enhance total revenue for sellers and total value for buyers.

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