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A Composable Game-Theoretic Framework for Blockchains

Zeta Avarikioti, Georg Fuchsbauer, Pim Keer, Matteo Maffei, Fabian Regen

TL;DR

The paper addresses incentive compatibility in multi-layer blockchain ecosystems where applications interact across the network and consensus layers. It introduces a composable game-theoretic framework with three layer-games—the blockchain game, the application game, and the network game—and two compositions: cross-layer and cross-application, enabling IC reasoning w.r.t. the blockchain behaviour $β$. The contributions include formal definitions of the three games, rigorous composition notions, and multiple case studies (e.g., HTLCs, Layer-2, and MEV) that surface cross-layer vulnerabilities and enable modular security proofs. The framework supports broad applications such as cross-application, cross-chain, and PBS contexts, offering a principled toolset for designing incentive-aligned, multi-protocol blockchain systems.

Abstract

Blockchains rely on economic incentives to ensure secure and decentralised operation, making incentive compatibility a core design concern. However, protocols are rarely deployed in isolation. Applications interact with the underlying consensus and network layers, and multiple protocols may run concurrently on the same chain. These interactions give rise to complex incentive dynamics that traditional, isolated analyses often fail to capture. We propose the first compositional game-theoretic framework for blockchain protocols. Our model represents blockchain protocols as interacting games across layers -- application, network, and consensus. It enables formal reasoning about incentive compatibility under composition by introducing two key abstractions: the cross-layer game, which models how strategies in one layer influence others, and cross-application composition, which captures how application protocols interact concurrently through shared infrastructure. We illustrate our framework through case studies on HTLCs, Layer-2 protocols, and MEV, showing how compositional analysis reveals subtle incentive vulnerabilities and supports modular security proofs.

A Composable Game-Theoretic Framework for Blockchains

TL;DR

The paper addresses incentive compatibility in multi-layer blockchain ecosystems where applications interact across the network and consensus layers. It introduces a composable game-theoretic framework with three layer-games—the blockchain game, the application game, and the network game—and two compositions: cross-layer and cross-application, enabling IC reasoning w.r.t. the blockchain behaviour . The contributions include formal definitions of the three games, rigorous composition notions, and multiple case studies (e.g., HTLCs, Layer-2, and MEV) that surface cross-layer vulnerabilities and enable modular security proofs. The framework supports broad applications such as cross-application, cross-chain, and PBS contexts, offering a principled toolset for designing incentive-aligned, multi-protocol blockchain systems.

Abstract

Blockchains rely on economic incentives to ensure secure and decentralised operation, making incentive compatibility a core design concern. However, protocols are rarely deployed in isolation. Applications interact with the underlying consensus and network layers, and multiple protocols may run concurrently on the same chain. These interactions give rise to complex incentive dynamics that traditional, isolated analyses often fail to capture. We propose the first compositional game-theoretic framework for blockchain protocols. Our model represents blockchain protocols as interacting games across layers -- application, network, and consensus. It enables formal reasoning about incentive compatibility under composition by introducing two key abstractions: the cross-layer game, which models how strategies in one layer influence others, and cross-application composition, which captures how application protocols interact concurrently through shared infrastructure. We illustrate our framework through case studies on HTLCs, Layer-2 protocols, and MEV, showing how compositional analysis reveals subtle incentive vulnerabilities and supports modular security proofs.

Paper Structure

This paper contains 31 sections, 7 theorems, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Layer-specific models.
  5. Model
  6. The Blockchain Game
  7. The Application Game
  8. The Network Game
  9. Composition
  10. Cross-layer Composition
  11. Cross-application Composition
  12. Illustrative Use Cases
  13. The Censor-Only Miner Game
  14. Timelock-based Games
  15. An HTLC in a Payment Channel
  16. ...and 16 more sections

Key Result

Theorem 3.3

Let $\beta$ be a blockchain behaviour and $\omega$ an additive execution function. Let $\Pi_1=(N_1,(\mathcal{A}^p_1)_{p\in\mathcal{P}},(\overline{\sigma}^p_{a,1})_{p\in \mathcal{P}})$ and $\Pi_2=(N_2,(\mathcal{A}^p_2)_{q\in\mathcal{Q}},(\overline{\sigma}^q_{a,2})_{q\in\mathcal{Q}})$ be two IC protoc

Figures (5)

  • Figure 1: Transaction flow for a CRAB PC
  • Figure 2: Tree for $K_{-1}$.
  • Figure 3: Tree for $K_t$ for $0\leq t\leq T$. If $t=T$, replace $K_{t+1}$ by $\varnothing$.
  • Figure :
  • Figure :

Theorems & Definitions (34)

  • Remark 2.1
  • definition 1
  • Remark 2.2
  • definition 2: Blockchain Game
  • definition 3: Fee function
  • definition 4: Censor-Only Miner Game (COMG)
  • definition 5: Application Game
  • definition 6
  • Remark 2.3
  • definition 7: Player function
  • ...and 24 more