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Effective Anonymous Messaging: the Role of Altruism

Marcell Frank, Balazs Pejo, Gergely Biczok

TL;DR

The paper investigates the viability of Fuzzy Message Detection (FMD) for anonymous messaging in the presence of altruistic users, using empirical game theory on real network data. It extends the selfish FMD model with local and global altruism, and analyzes equilibria via best-response dynamics, showing that a small number of altruists can yield non-trivial equilibria and move the system closer to social optimum. The authors demonstrate that betweenness centrality can guide mechanism design to approach the social optimum, while highlighting PoA being high and PoS lower, indicating efficiency losses under selfish behavior. Practical deployment considerations and limitations are discussed, including dynamic networks and secure computation for central control, with future work suggested on bounded rationality and broader protocol generalization.

Abstract

Anonymous messaging and payments have gained momentum recently due to their impact on individuals, society, and the digital landscape. Fuzzy Message Detection (FMD) is a privacy-preserving protocol where an untrusted server performs message anonymously filtering for its clients. To prevent the server from linking the sender and the receiver, the latter can set how much cover traffic they should download along with genuine messages. This could cause unwanted messages to appear on the user's end, thereby creating a need to balance one's bandwidth cost with the desired level of unlinkability. Previous work showed that FMD is not viable with selfish users. In this paper, we model and analyze FMD using the tools of empirical game theory and show that the system needs at least a few altruistic users to operate properly. Utilizing real-world communication datasets, we characterize the emerging equilibria, quantify the impact of different types and levels of altruism, and assess the efficiency of potential outcomes versus socially optimal allocations. Moreover, taking a mechanism design approach, we show how the betweenness centrality (BC) measure can be utilized to achieve the social optimum.

Effective Anonymous Messaging: the Role of Altruism

TL;DR

The paper investigates the viability of Fuzzy Message Detection (FMD) for anonymous messaging in the presence of altruistic users, using empirical game theory on real network data. It extends the selfish FMD model with local and global altruism, and analyzes equilibria via best-response dynamics, showing that a small number of altruists can yield non-trivial equilibria and move the system closer to social optimum. The authors demonstrate that betweenness centrality can guide mechanism design to approach the social optimum, while highlighting PoA being high and PoS lower, indicating efficiency losses under selfish behavior. Practical deployment considerations and limitations are discussed, including dynamic networks and secure computation for central control, with future work suggested on bounded rationality and broader protocol generalization.

Abstract

Anonymous messaging and payments have gained momentum recently due to their impact on individuals, society, and the digital landscape. Fuzzy Message Detection (FMD) is a privacy-preserving protocol where an untrusted server performs message anonymously filtering for its clients. To prevent the server from linking the sender and the receiver, the latter can set how much cover traffic they should download along with genuine messages. This could cause unwanted messages to appear on the user's end, thereby creating a need to balance one's bandwidth cost with the desired level of unlinkability. Previous work showed that FMD is not viable with selfish users. In this paper, we model and analyze FMD using the tools of empirical game theory and show that the system needs at least a few altruistic users to operate properly. Utilizing real-world communication datasets, we characterize the emerging equilibria, quantify the impact of different types and levels of altruism, and assess the efficiency of potential outcomes versus socially optimal allocations. Moreover, taking a mechanism design approach, we show how the betweenness centrality (BC) measure can be utilized to achieve the social optimum.
Paper Structure (16 sections, 1 theorem, 3 equations, 3 figures, 1 table)

This paper contains 16 sections, 1 theorem, 3 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Preliminaries
  4. Related Work
  5. Model
  6. The Selfish Game
  7. The Altruistic Game
  8. Experiments
  9. Datasets
  10. Best-response dynamics
  11. Initial strategy candidates for BRD
  12. Results
  13. Social Optimum
  14. Equilibrium Analysis
  15. Equilibrium versus Social Optimum
  16. ...and 1 more sections

Key Result

theorem thmcountertheorem

The only NE for the FMD Game is where no one utilizes any cover traffic, i.e., $p_u=0$ for all $1\le u\le U$.

Figures (3)

  • Figure 1: FMD failure: Recipient D has seemingly maximum protection because it downloads all messages as cover traffic, yet its genuine message (white envelope) is not downloaded by any other participants, so no relationship anonymity is provided.
  • Figure 2: SO without altruism, uniform false positive rates.
  • Figure 3: "Empirical CDF" of aggregated betw. centr. over users ordered by decreasing cover traffic for SO and best-case NE.

Theorems & Definitions (7)

  • definition thmcounterdefinition: FMD Game
  • theorem thmcountertheorem: Seres, Pejó, and Burcsi seres2022effect
  • definition thmcounterdefinition: Altruistic player
  • definition thmcounterdefinition: L-FMD Game
  • definition thmcounterdefinition: G-FMD Game
  • definition thmcounterdefinition: Betweenness Centrality (BC) freeman1977set
  • definition thmcounterdefinition: $\varepsilon$-BRD (Maximum Gain) roughgarden_2016