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Pessimism of the Will, Optimism of the Intellect: Fair Protocols with Malicious but Rational Agents

Léonard Brice, Jean-François Raskin, Mathieu Sassolas, Guillaume Scerri, Marie van den Bogaard

TL;DR

This work presents a game-based framework for the study of fairness protocols, that does not define a priori an attacker model, and is based on the notion of strong secure equilibria, and leverages the conceptual and algorithmic toolbox of game theory.

Abstract

Fairness is a desirable and crucial property of many protocols that handle, for instance, exchanges of message. It states that if at least one agent engaging in the protocol is honest, then either the protocol will unfold correctly and fulfill its intended goal for all participants, or it will fail for everyone. In this work, we present a game-based framework for the study of fairness protocols, that does not define a priori an attacker model. It is based on the notion of strong secure equilibria, and leverages the conceptual and algorithmic toolbox of game theory. In the case of finite games, we provide decision procedures with tight complexity bounds for determining whether a protocol is immune to nefarious attacks from a coalition of participants, and whether such a protocol could exist based on the underlying graph structure and objectives.

Pessimism of the Will, Optimism of the Intellect: Fair Protocols with Malicious but Rational Agents

TL;DR

This work presents a game-based framework for the study of fairness protocols, that does not define a priori an attacker model, and is based on the notion of strong secure equilibria, and leverages the conceptual and algorithmic toolbox of game theory.

Abstract

Fairness is a desirable and crucial property of many protocols that handle, for instance, exchanges of message. It states that if at least one agent engaging in the protocol is honest, then either the protocol will unfold correctly and fulfill its intended goal for all participants, or it will fail for everyone. In this work, we present a game-based framework for the study of fairness protocols, that does not define a priori an attacker model. It is based on the notion of strong secure equilibria, and leverages the conceptual and algorithmic toolbox of game theory. In the case of finite games, we provide decision procedures with tight complexity bounds for determining whether a protocol is immune to nefarious attacks from a coalition of participants, and whether such a protocol could exist based on the underlying graph structure and objectives.
Paper Structure (41 sections, 11 theorems, 16 equations, 15 figures, 1 table)

This paper contains 41 sections, 11 theorems, 16 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Rationality in games
  3. Approach and contributions
  4. Related Works
  5. The challenges of fair exchange
  6. With a trusted third party
  7. Beyond trust: without a trusted third party
  8. General formalisms
  9. Framework
  10. Safe protocols as strong secure equilibria
  11. Finite models of protocols
  12. About compliant infrastructures
  13. Modeling message exchanges in games
  14. Protocol challenges for message exchange
  15. The Zhou-Gollmann optimistic protocol
  16. ...and 26 more sections

Key Result

Theorem 1

Let $\mathcal{C}$ be a protocol challenge, and let us consider the game $\mathcal{G}$ defined as follows: the players are the agents of $\mathcal{C}$, the strategies available for each player $i$ are the behaviors available for agent $a$ in $\mathcal{C}$, and the payoff functions are defined as foll Then, the protocol $P$ is safe if and only if each $\bar{\sigma} \in P$ is an SSE satisfying $\mu_i

Figures (15)

  • Figure 1: Expected exchanged items between Alice, Bob, and Charlie.
  • Figure 2: Mealy machine $\mathcal{M}_\theta$ for the Zhou-Gollmann Protocol. $\theta$ specifies the number of steps each agent is allowed until the deadline $t$ is reached.
  • Figure 3: Arena for the exchange of items between three players (partial depiction).
  • Figure 4: Büchi automaton $\mathcal{A}_{\mathbb{A}}$ in the tripartite exchange of items protocol challenge (partial depiction). Doubly rounded states are accepting.
  • Figure 5: Game $\mathcal{G}_\varphi$ to encode the satisfiability of propositional formula $\varphi$ into a game.
  • ...and 10 more figures

Theorems & Definitions (46)

  • Definition 1: Protocol challenge
  • Definition 2: Protocol, implementation
  • Example 1
  • Definition 3: Attack, safe protocol
  • Remark 1
  • Definition 4
  • Example 2
  • Example 3
  • Definition 5: Game
  • Definition 6: Strong secure equilibrium
  • ...and 36 more