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Fair Combinatorial Auction for Blockchain Trade Intents: Being Fair without Knowing What is Fair

Andrea Canidio, Felix Henneke

TL;DR

The paper analyzes trade-intent auctions on permissionless blockchains, where combinatorial execution yields efficiency but raises fairness concerns about how to share gains from batching. It introduces an endogenous fairness benchmark built from individual-trade bids and proposes the fair combinatorial auction, which filters batched bids that do not improve all traders relative to the benchmark. The equilibrium analysis shows that second-price individual-order auctions offer no extra fairness guarantees beyond batching, while first-price individual-order auctions can deliver strong fairness guarantees, albeit with an efficiency cost. The results highlight a fairness-efficiency tradeoff and suggest extensions to multi-trader settings and sequential designs for blockchain-based markets.

Abstract

We study blockchain trade-intent auctions, which currently intermediate about USD 10 billion in trades each month. These auctions are combinatorial because executing multiple trade intents jointly generates additional efficiencies. However, the auctioneer cannot observe what each trader would have received had its order been auctioned individually and hence cannot determine how these efficiencies should be shared. We compare the two dominant mechanisms - batch auctions and simultaneous individual auctions - and introduce a novel definition of fairness applicable to combinatorial auctions. We then propose a fair combinatorial auction that endogenously constructs a fairness benchmark from individual bids and a counterfactual mechanism. Whether fairness guarantees arise in equilibrium depends on the counterfactual: all traders receive more in the equilibrium of the fair combinatorial auction than in the equilibrium of the counterfactual mechanism when the counterfactual is simultaneous first-price auctions, but that may not be the case if the counterfactual is simultaneous second-price auctions.

Fair Combinatorial Auction for Blockchain Trade Intents: Being Fair without Knowing What is Fair

TL;DR

The paper analyzes trade-intent auctions on permissionless blockchains, where combinatorial execution yields efficiency but raises fairness concerns about how to share gains from batching. It introduces an endogenous fairness benchmark built from individual-trade bids and proposes the fair combinatorial auction, which filters batched bids that do not improve all traders relative to the benchmark. The equilibrium analysis shows that second-price individual-order auctions offer no extra fairness guarantees beyond batching, while first-price individual-order auctions can deliver strong fairness guarantees, albeit with an efficiency cost. The results highlight a fairness-efficiency tradeoff and suggest extensions to multi-trader settings and sequential designs for blockchain-based markets.

Abstract

We study blockchain trade-intent auctions, which currently intermediate about USD 10 billion in trades each month. These auctions are combinatorial because executing multiple trade intents jointly generates additional efficiencies. However, the auctioneer cannot observe what each trader would have received had its order been auctioned individually and hence cannot determine how these efficiencies should be shared. We compare the two dominant mechanisms - batch auctions and simultaneous individual auctions - and introduce a novel definition of fairness applicable to combinatorial auctions. We then propose a fair combinatorial auction that endogenously constructs a fairness benchmark from individual bids and a counterfactual mechanism. Whether fairness guarantees arise in equilibrium depends on the counterfactual: all traders receive more in the equilibrium of the fair combinatorial auction than in the equilibrium of the counterfactual mechanism when the counterfactual is simultaneous first-price auctions, but that may not be the case if the counterfactual is simultaneous second-price auctions.
Paper Structure (23 sections, 7 theorems, 35 equations, 2 figures, 1 table)

This paper contains 23 sections, 7 theorems, 35 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Relevant literature
  3. The model
  4. Production possibility frontier.
  5. Feasibility constraint.
  6. Information.
  7. Payoffs.
  8. Timing.
  9. Mechanism.
  10. Examples: Batch auctions and simultaneous standard auctions
  11. Simultaneous standard auctions
  12. Batch auction
  13. Fair combinatorial auctions.
  14. Equilibrium of the fair combinatorial auction
  15. Second-price individual auctions
  16. ...and 8 more sections

Key Result

Lemma 1

If there are two simultaneous standard auctions, then every equilibrium of the auction, solver 1 wins the first order and returns at most $\underline\beta$ units of asset $B$, while solver 2 wins the second order and returns at most $\underline\delta$ units of asset $D$.

Figures (2)

  • Figure 1: The two best responses (note: we only consider the bids not already pinned down by Lemma \ref{['lem: intermediate']})
  • Figure 2: Solvers' production possibilities when matched with both orders (red and green dots) and when matched with a single order (black dot). The shaded areas are the sets of feasible transfers in case a solver wins both orders, as a function of the choice of production. On the top, $p_{DB}$ is low and $\{k \cdot \underline\beta, \tau \underline\delta\}$ generates higher value than the alternative; on the bottom $p_{DB}$ is high and $\{k \cdot \underline\beta, \tau \underline\delta\}$ generates lower value than the alternative.

Theorems & Definitions (16)

  • Definition 1: Feasible mechanism
  • Lemma 1
  • Lemma 2
  • Remark 1
  • Definition 2: Outcome determined by individual bids
  • Definition 3: Fairness
  • Lemma 3
  • Definition 4: Fair batched bid
  • Lemma 4
  • Lemma 5
  • ...and 6 more