Introduction
In this post, I want to provide a brief summary of our most recent paper, “The Candle Auction in the Field and the Lab” that is co-authored with Samuel Häfner (University of St.Gallen and formerly W3F researcher) and Jörg Oechssler (Professor at University of Heidelberg). The paper is openly accessible, and I encourage everyone to take a look. Although the candle auctions in their original form were deprecated on Polkadot in October 2024, the insights gained from analyzing them remain highly valuable for shaping the future of digital marketplaces.
In our study, we provide a holistic analysis of the candle auction mechanism from theoretical, empirical, and experimental perspectives. Results from each approach paint a concise and unified picture of the mechanism’s effectiveness.
In this short overview, I focus on the efficiency and revenue analyses of the auctions in both the Polkadot/Kusama setting and our experimental study. In the paper, we also explore the combinatorial aspects of the auctions, their robustness to collusion, and offer a comprehensive theoretical analysis. These additional topics go beyond the scope of this post, so I once again encourage interested readers to check out the full paper for more details.
Note: A shout-out to Parity’s data team for supporting me in getting the data for the empirical analysis!
Primer on Candle Auctions and Auction Theory
Candle auctions, introduced in the 16th century, relied on bidding until a candle went out, making the end time unpredictable and discouraging sniping. Though rarely being applied in history, their first wide application was in Polkadot and Kusama’s parachain slot auctions (2021–2024), which used a fixed bidding period but randomly determined the actual ending block.
Two key metrics help evaluate auctions. First, efficiency, meaning the highest-valuation bidder wins. Since valuations (i.e., how much a bidder is willing to pay) are private, good auction design should encourage truthful bidding to ensure efficient outcomes. Second, revenue, or how bids translate into payments. Common rules include first-price (the winning bidder pays their own bid) and second-price (the winning bidder pays the second-highest bid).
We aim to design mechanisms that achieve both efficiency and high revenue. However, in a random-ending auction, if bidders place late bids and the auction closes prematurely, the outcome may fail on both counts—potentially awarding the item to a lower-valuation bidder at a suboptimal price. Our study examines these effects in detail from multiple perspectives.
Results
In this section, I am presenting some of the main results of the empirical- and experimental analysis.
Empirical Evidence
We analyzed 70 auctions on Polkadot (n=15) and Kusama (n=55) between June 2022 and August 2024. We excluded auctions involving crowdloans, since the additional incentive layer for users invalidates our normal bidding assumptions (e.g., bidders typically seek to obtain the good at the lowest price possible). We also removed auctions that had only one or no bidders, because our measures do not make sense in the absence of competitive bidding. As a sidenote, including crowdloans into our analysis lead to similarly (if not better) results.
Our primary focus is on efficiency and relative revenue:
- Relative revenue is defined as the ratio of the winning bid combination to the hypothetical bid combination that would have won at the very end of the auction.
- Efficiency is the ratio of the highest bid combination from the winner to that same hypothetical final bid combination.
The results on these auctions are shown below:
The candle auctions performed strongly, achieving average efficiencies of 97.4% on Polkadot and 89.9% on Kusama. Relative revenue, though slightly lower than optimal, was 83.9% on Polkadot and 77.7% on Kusama, meaning about 16% fewer tokens were locked on Polkadot and 24% on Kusama than might have been possible. Overall, this still reflects a successful outcome, as bidders adapted to the mechanism’s incentives by bidding early.
Below is a graph of the average relative winning bids (the ratio of the current winning bid to the highest observed winning bid), with dashed lines marking the end of the grace period (red) and halfway through the ending phase (yellow).
From the graph we can see that, on average, at around half of the duration of the auction, bids already were around 80% of their respective maximum.
To summarize, the candle auctions on Polkadot and Kusama performed very well and allocated the slots efficiently and gathered sufficient revenue.
Experiment
While the empirical results for Polkadot and Kusama’s candle auctions appear strong, two key limitations remain. First, we lack a direct comparison to other established auction formats, which might have performed as well or better. Second, because valuations are private, we relied on bidders’ highest submitted bids as proxies for their true valuations. To address these issues, we conducted a laboratory experiment at the University of Heidelberg with 162 students, where valuations were precisely controlled. This allowed us to directly compare candle auctions against a traditional “hard close” format (with a fixed ending time) and an “activity rule” or “softclose” format (which extends the auction if a late bid arrives). The study was funded by a Treasury grant. The different formats worked as follows:
- Candle: Bidders place increasing bids during a 60-second fixed time window, but the actual ending moment is randomly chosen (retrospectively) after the first 15 seconds and the 60th second. Whoever leads at that random time wins and pays their bid.
- Hard: Bidders place increasing bids during a 60-second fixed time window. Whoever leads at that 60th second wins and pays their bid.
- Activity: Bidders place increasing bids during a 45-second fixed time window and the end of the auction would be increased by 10 seconds if another highest bid was submitted. Whoever leads at that random time wins and pays their bid.
We randomly allocated students into groups of three and had them play ten consecutive rounds. We randomly allocated valuations to each bidder within some bounds and bidders would earn money depending on the difference between their bid and their valuation. We also allowed them to communicate before each auction, allowing the possibility for collusion (check the paper for more info).
The results are:
From these findings, efficiency and relative revenue are statiscially equal across the different auction formats, implying that the candle mechanism is at least on par with traditional auctions. Remarkably, collusive agreements in our chat data were significantly less frequent under the candle rule, suggesting it offers some resistance to collusion.
Below is the same type of average relative winning-bid graph as before.
Notably, it matches our empirical observations: bids escalate early under the candle mechanism, yielding favorable outcomes. In contrast, the soft-close format (activity) demonstrates how an auction’s length becomes unpredictable and endogenously determined, posing practical scheduling challenges in more time-sensitive contexts.
Conclusion
In conclusion, our theoretical, empirical, and experimental work on candle auctions indicates that, despite the random ending time, the format delivers comparable (if not superior) efficiency and revenue to standard auctions while providing notable resistance to collusion. Our findings underscore the robustness and practical viability of candle auctions in modern digital marketplaces, especially where open communication channels can pose significant challenges.
Further Reading
- Our Paper on Candle Auctions.
- Contemporary historical account on first and second batch of auctions on Kusama and first batch on Polkadot.
- A case for Candle Auctions on Blockchain