Incentive Schemes for Rollup Validators

TL;DR

This paper introduces a game-theoretic framework for incentivizing validators in rollup systems, analyzing equilibrium strategies and optimizing validator count and stake sizes for enhanced security.

Contribution

It develops a novel incentive scheme model for rollup validators, providing analytical bounds and strategies for optimal validator participation and reward design.

Findings

Pure strategy Nash equilibrium does not exist without outside parties.

Optimal validator number minimizes failure probability.

Stake size and reward schemes can be optimized for security.

Abstract

We design and analyze attention games that incentivize validators to check computation results. We show that no pure strategy Nash equilibrium of the game without outside parties exists by a simple argument. We then proceed to calculate the security of the system in the mixed Nash equilibrium, as a function of the number of validators and their stake sizes. Our results provide lower and upper bounds on the optimal number of validators. More concretely, a minimal feasible number of validators minimizes the probability of failure. The framework also allows to calculate optimum stake sizes, depending on the target function. In the end, we discuss optimal design of rewards by the protocol for validators.