Auction Design and Price Discovery in Decentralized Markets

View Slides & Handout on Zenodo

This post is based on a seminar I gave at the National University of Singapore on April 14, 2026.

Auctions aggregate dispersed private information (each bidder's valuation) into a single clearing price, making them central to price discovery and allocation of digital assets. Before a continuous secondary market exists, a single-sided discrete auction must establish the initial clearing price: the cold-start problem. This lecture focuses on single-sided discrete formats, before the transition to continuous secondary trading.

Auction theory

Auctions are non-cooperative games with incomplete information: each bidder optimizes their bid knowing their own valuation but not those of competitors. The game-theoretic foundations build on Von Neumann and Morgenstern, Nash, and Myerson.

A player's utility is quasi-linear if it can be expressed as

$$U_i : \theta_i \mapsto \theta_i x_i(\theta_i) - p_i(\theta_i)$$

where $\theta_i$ is the player's type, $x_i(\theta_i) \in [0, 1]$ is the interim allocation rule, and $p_i(\theta_i)$ is the payment function. Here $x_i(\theta_i) \in [0, 1]$ is the probability of receiving the item, $p_i(\theta_i)$ is the amount paid, and net benefit scales linearly with the allocation relative to private value.

A mechanism satisfies individual rationality (IR) if every player obtains a non-negative expected payoff from participating, i.e. $U_i(\theta_i) \ge 0$ for all types. IR ensures voluntary participation: no one joins a game where they expect to lose. A mechanism is incentive compatible (IC) if, for each player and type, truthful reporting maximizes expected payoff. IC is the binding constraint for auction design. A mechanism is dominant-strategy incentive compatible (DSIC) if, for every player $i$ and every type $\theta_i$, reporting $\theta_i$ truthfully is a dominant strategy. When a mechanism is DSIC, bidders have no reason to shade their bids, regardless of what competitors do.

The interim allocation rule $x_i(\theta_i)$ of any IC mechanism must be non-decreasing: higher types must win the item at least as often as lower types. IC ensures truth-telling is optimal; IR ensures voluntary participation is rational; non-decreasing $x_i$ is the structural consequence of IC, explaining why the highest bid wins in all four classical formats.

The Revenue Equivalence Theorem

Under independent private values (IPV), symmetry, and risk neutrality, any two mechanisms that implement the same interim allocation rule and give the same expected utility to the lowest type generate the same expected revenue for the seller.

A numerical check with 3 bidders (types $v_i \sim U[0, 1]$) confirms this. In a Vickrey auction, bidders bid truthfully and the winner pays the second-order statistic: $E[\text{revenue}] = (n-1)/(n+1) = 0.5$. In a first-price auction, the symmetric BNE bid is $b(v) = (n-1)/n \cdot v = 2/3 v$, and the winner pays their own shaded bid: $E[\text{revenue}] = 2/3 \cdot n/(n+1) = 0.5$. Both formats allocate to the highest type and yield the same expected revenue. Format is irrelevant; the allocation rule drives revenue.

When bidders' signals are affiliated (positively correlated), RET breaks down. Milgrom & Weber prove the ranking: English $\ge$ Vickrey $\ge$ First-price = Dutch. The Linkage Principle explains why: linking the winner's payment to additional information affiliated with bidders' signals raises expected revenue. English auction dropout prices provide this linkage; sealed-bid formats do not.

The four classical formats

*Japanese model (continuous clock, no jump bids). With discrete jump bids DSIC does not hold exactly.

English auction. An open process in which bids increase sequentially until no higher bids are forthcoming. In the canonical Japanese model, remaining active until the price reaches one's true value is weakly dominant (DSIC). English auctions dominate NFT primary sales, but pseudonymous sellers submit shill bids at negligible cost, eroding information value and pushing honest bidders toward sealed-bid strategies.

Dutch auction. Starts at a high asking price and descends until a bidder accepts. The BNE strategy is to accept at a price below one's true value, with shading depending on beliefs about competitors. Dutch and first-price auctions are strategically isomorphic and revenue-equivalent under IPV.

Sealed-bid (first-price). Bids are collected independently and without revelation until close. In symmetric BNE, bidders shade below their true value. On Ethereum, Priority Gas Auctions mirror this format: MEV bots bid up gas fees for execution priority, but the public mempool makes the dynamics closer to an ascending auction; bots observe each other's bids and outbid in real time.

Vickrey (second-price sealed-bid). The highest bidder wins but pays the second-highest bid. Truthful bidding is weakly dominant (DSIC). Under IPV, Vickrey is isomorphic to the English auction in allocation and expected revenue. Vickrey auctions are rarely used on-chain: pseudonymous sellers deploy multiple wallets to inflate the second-highest bid, breaking DSIC.

For $n$ symmetric bidders with types $v_i \sim U[0, 1]$, the first-price equilibrium bid is:

$$b(v) = \frac{n-1}{n}v$$

As $n \to \infty$, $b(v) \to v$; competition eliminates shading. In common-value settings, winning reveals that all rivals valued the item less (the winner's curse), so rational bidders shade further. The Linkage Principle offers mitigation: a seller who credibly discloses affiliated information (appraisals, oracle price feeds) reduces the curse and raises expected revenue.

Why format matters on-chain

Under classical assumptions, the allocation rule determines expected revenue regardless of format. On-chain, those assumptions fail: validators reorder transactions, the mempool is public, and pseudonymity enables collusion, making the allocation rule unenforceable. Format choice matters again, not because allocation rules change, but because format determines whether they can be enforced. No classical format survives these violations unchanged.

Key Insight. Under classical assumptions, the allocation rule determines expected revenue regardless of format. On-chain, format determines whether the allocation rule is enforceable.

Batch auctions

Given these systematic vulnerabilities, batch auctions offer an alternative. A batch auction accumulates bids and offers over a fixed interval $[0, \Delta t]$, then clears all orders simultaneously at a uniform equilibrium price. Because the clearing price is order-independent, participants cannot gain a reordering advantage within the batch, eliminating reordering-based MEV. In the single-unit case, uniform pricing restores the weak dominance of truthful bidding; in multi-unit settings, demand reduction incentives remain.

As $\Delta t \to 0$, batch auctions converge to continuous double auctions (limit order books). A Continuous Clearing Auction (CCA), in Uniswap's terminology, is a batch auction where $\Delta t$ equals one blockchain block ($\approx 12$ seconds on Ethereum), providing a structural defence against MEV.

Example (Algorand, 2019). Algorand distributed 25M ALGO via a Dutch auction clearing at $2.40, the uniform-price variant of the multi-unit Dutch auction. The clearing price exceeded sellers' internal estimates, but ALGO fell ~90% within months. Auction price discovery does not guarantee sustainable secondary-market valuation.

Research gaps

Formal auction theory for DeFi remains under-developed. The canonical IPV model provides tractable benchmarks, but DeFi assets carry common-value components, gas-fee frictions, and on-chain constraints that break classical assumptions. Interdependent-value models, on-chain sealed-bid mechanisms, budget constraints with latency costs, and equilibrium properties of batch/CCA mechanisms are all open areas. Large-population auctions and mean-field games could simplify analysis for NFT drops and token launches but are not yet established for discrete DeFi auctions.

Key takeaways

• Auctions are the primary price discovery mechanism for primary distributions in DeFi, before fragmented continuous secondary markets emerge.
• Classical theory: under RET, the allocation rule determines revenue regardless of format.
• On-chain twist: blockchain constraints (bid visibility, gas costs, validator reordering) make the allocation rule unenforceable; format now determines whether outcomes follow the rule at all.
• Batch auctions mitigate reordering-based MEV through uniform pricing; cross-batch MEV and shill bidding remain open.
• The literature on DeFi auction design is thin: interdependent values, on-chain sealed bids, gas frictions, large-population settings, and equilibrium properties of batch/CCA mechanisms are all open areas.

The lecture slides and handout are available on Zenodo.