Incentive Mechanism Design for Privacy-Preserving Decentralized Blockchain Relayers

TL;DR

The paper tackles privacy in public blockchains by decentralizing the relayer layer and designing a game-theoretic incentive mechanism that induces indistinguishable probabilistic uploads. Modeling relayers as a symmetric N-player game inspired by the Volunteer's Dilemma, it proves the existence and uniqueness of a symmetric mixed Nash equilibrium with upload probability $q_u^*$ and shows asymptotic stability under evolutionary dynamics. Numerical results reveal a fundamental trade-off: increasing the number of relayers enlarges the anonymity set and improves privacy but raises outage probability, while stronger penalties improve participation and reliability at the cost of robustness and economic feasibility. The framework offers a practical design for privacy-preserving, incentive-compatible decentralized relayer architectures in blockchain systems, with clear guidance on parameter tuning and trade-offs for real deployments.

Abstract

Public blockchains, though renowned for their transparency and immutability, suffer from significant privacy concerns. Network-level analysis and long-term observation of publicly available transactions can often be used to infer user identities. To mitigate this, several blockchain applications rely on relayers, which serve as intermediary nodes between users and smart contracts deployed on the blockchain. However, dependence on a single relayer not only creates a single point of failure but also introduces exploitable vulnerabilities that weaken the system's privacy guarantees. This paper proposes a decentralized relayer architecture that enhances privacy and reliability through game-theoretic incentive design. We model the interaction among relayers as a non-cooperative game and design an incentive mechanism in which probabilistic uploading emerges as a unique mixed Nash equilibrium. Using evolutionary game analysis, we demonstrate the equilibrium's stability against perturbations and coordinated deviations. Through numerical evaluations, we analyze how equilibrium strategies and system behavior evolve with key parameters such as the number of relayers, upload costs, rewards, and penalties. In particular, we show that even with high transaction costs, the system maintains reliability with an outage probability below 0.05 . Furthermore, our results highlight a fundamental trade-off between privacy, reliability, robustness, and cost in decentralized relayer systems.

Figures (6)

• Figure 1: Illustration of the decentralized relayer model.
• Figure 2: Equilibrium upload probability $q_u^*$, outage probability $P_O^*$ and expected reward $R^*$ as a function of N, with $b=100$, $c_l=1$, $p=100$ and $c_f= 25,50$ and $75$.(a) Upload Probability at equilibrium. (b) Probability of outage at equilibrium. (c) Expected reward at equilibrium.
• Figure 3: Equilibrium upload probability $q_u^*$, outage probability $P_O^*$ and expected reward $R^*$ as a function of the unit of cost $c_l$, with $b=100$, $c_f=50$, $p=100$ and $N= 5,10$ and $30$.(a) Upload probability at equilibrium. (b) Probability of outage at equilibrium. (c) Expected reward at equilibrium.
• Figure 4: Equilibrium upload probability $q_u^*$, outage probability $P_O^*$ and expected reward $R^*$ as a function of the penalty $p$, with $b=100$, $c_f=50$, $c_l=25$ and $N= 5,10$ and $30$.(a) Upload probability at equilibrium. (b) Probability of outage at equilibrium. (c) Expected reward at equilibrium.
• Figure 5: Evolution of the upload probability $q_u(t)$ under the replicator’s dynamic with parameters $b=100$, $c_f=25$, $c_l=1$, $p=100$, and $\mu=0.1$. The trajectories are shown for different initial states $q_u(0)= 0.10$,$0.50$ and for different values of $N$. (a) $N=5$, (b) $N=10$, and (c) $N=30$.

Theorems & Definitions (13)

• Definition 1: Nash Equilibrium, SAMSON_CHAP1
• Theorem 1
• Definition 2: Exact Potential Game, SAMSON_CHAP2
• Proposition 1
• Definition 3: $\alpha$-Strong Equilibrium, SAMSON_CHAP1
• Proposition 2: $N-$strong equilibria of the relayer upload game
• Corollary 1
• Proposition 3: Evolutionary Stability and Invasion Barrier
• proof
• proof