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Shapley Value-based Approach for Redistributing Revenue of Matchmaking of Private Transactions in Blockchains

Rasheed, Parth Desai, Yash Chaurasia, Sujit Gujar

TL;DR

The paper addresses fair revenue redistribution in MEV matchmaking by formulating the RST-Game, a cooperative game over transaction creators, and applying Shapley value-based allocations. It proves that Shapley values are computable in polynomial time under additive searcher valuations, while single-minded valuations induce SUBEXP hardness, motivating a randomized approximation method (RSYP) with provable error properties. RSYP, validated on extensive simulations, closely matches exact Shapley-based redistributions with polynomially bounded sample size, offering a practical mechanism for equitable revenue sharing. The work advances MEV matchmaking by delivering a principled fairness criterion, concrete algorithms, and empirical evidence supporting real-world deployment potential.

Abstract

In the context of blockchain, MEV refers to the maximum value that can be extracted from block production through the inclusion, exclusion, or reordering of transactions. Searchers often participate in order flow auctions (OFAs) to obtain exclusive rights to private transactions, available through entities called matchmakers, also known as order flow providers (OFPs). Most often, redistributing the revenue generated through such auctions among transaction creators is desirable. In this work, we formally introduce the matchmaking problem in MEV, its desirable properties, and associated challenges. Using cooperative game theory, we formalize the notion of fair revenue redistribution in matchmaking and present its potential possibilities and impossibilities. Precisely, we define a characteristic form game, referred to as RST-Game, for the transaction creators. We propose to redistribute the revenue using the Shapley value of RST-Game. We show that the corresponding problem could be SUBEXP (i.e. $2^{o(n)}$, where $n$ is the number of transactions); therefore, approximating the Shapley value is necessary. Further, we propose a randomized algorithm for computing the Shapley value in RST-Game and empirically verify its efficacy.

Shapley Value-based Approach for Redistributing Revenue of Matchmaking of Private Transactions in Blockchains

TL;DR

The paper addresses fair revenue redistribution in MEV matchmaking by formulating the RST-Game, a cooperative game over transaction creators, and applying Shapley value-based allocations. It proves that Shapley values are computable in polynomial time under additive searcher valuations, while single-minded valuations induce SUBEXP hardness, motivating a randomized approximation method (RSYP) with provable error properties. RSYP, validated on extensive simulations, closely matches exact Shapley-based redistributions with polynomially bounded sample size, offering a practical mechanism for equitable revenue sharing. The work advances MEV matchmaking by delivering a principled fairness criterion, concrete algorithms, and empirical evidence supporting real-world deployment potential.

Abstract

In the context of blockchain, MEV refers to the maximum value that can be extracted from block production through the inclusion, exclusion, or reordering of transactions. Searchers often participate in order flow auctions (OFAs) to obtain exclusive rights to private transactions, available through entities called matchmakers, also known as order flow providers (OFPs). Most often, redistributing the revenue generated through such auctions among transaction creators is desirable. In this work, we formally introduce the matchmaking problem in MEV, its desirable properties, and associated challenges. Using cooperative game theory, we formalize the notion of fair revenue redistribution in matchmaking and present its potential possibilities and impossibilities. Precisely, we define a characteristic form game, referred to as RST-Game, for the transaction creators. We propose to redistribute the revenue using the Shapley value of RST-Game. We show that the corresponding problem could be SUBEXP (i.e. , where is the number of transactions); therefore, approximating the Shapley value is necessary. Further, we propose a randomized algorithm for computing the Shapley value in RST-Game and empirically verify its efficacy.

Paper Structure

This paper contains 23 sections, 6 theorems, 33 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Matchmaking
  5. Searcher-Matchmaker Auctions
  6. Towards Matchmaking Mechanism
  7. Characteristic Form Games and Shapley Value
  8. Our Approach
  9. RST-Game
  10. Shapley Value of RST-Game with Additive Valuation Searchers
  11. Shapley Value of RST-Game for Single-Minded Searchers
  12. Approximating Shapley Value
  13. Error Analysis
  14. Experimental Analysis
  15. Setup
  16. ...and 8 more sections

Key Result

Theorem 1

The Shapley value of RST-Game ($\mathcal{T},\nu$)) can be computed in polynomial time if $\nu$ is additive.

Figures (4)

  • Figure 1: Private Transactions on Ethereum dunePOF
  • Figure 2: Distribution of $\Gamma^{\texttt{RSYP}\ },\Gamma^{\texttt{SHAP}\ }$ vs $n$ for $m=6$
  • Figure 3: Distribution of $\Gamma^{\texttt{RSYP}\ },\Gamma^{\texttt{SHAP}\ }$ vs $m$ for $n=6$
  • Figure 4: Variation of Unique Marginal Contributions

Theorems & Definitions (16)

  • Definition 1: Matchmaking
  • Definition 2: Additive Valuations
  • Definition 3: Single-minded Valuations
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Conjecture 1
  • Theorem 3
  • proof
  • ...and 6 more