Coalition-Safe Equilibria with Virtual Payoffs

TL;DR

This paper introduces a new concept of coalition-safe equilibrium with virtual payoffs, analyzing incentives and stability in blockchain protocols, including Bitcoin and Fruitchain, under various utility functions and collusion scenarios.

Contribution

It defines coalition-safe equilibrium with virtual payoffs and applies it to blockchain protocols, providing new insights into incentive compatibility and collusion resistance.

Findings

Fruitchain protocol is stable against collusions of up to n-1 players for absolute rewards.

Fruitchain protocol is stable against collusions of less than n/2 players for relative rewards.

Introduces the property of 'weakly fair' blockchain protocols, relevant for incentive analysis.

Abstract

Consider a set of parties invited to execute a protocol $\Pi$. The protocol will incur some cost to run while in the end (or at regular intervals), it will populate and update local tables that assign (virtual) rewards to participants. Each participant aspires to offset the costs of participation by these virtual payoffs that are provided in the course of the protocol. In this setting, we introduce and study a notion of coalition-safe equilibrium. In particular, we consider a strategic coalition of participants that is centrally coordinated and potentially deviates from $\Pi$ with the objective to increase its utility with respect to the view of {\em at least one} of the other participants. The protocol $\Pi$ is called a coalition-safe equilibrium with virtual payoffs (EVP) if no such protocol deviation exists. We apply our notion to study incentives in blockchain protocols. We proceed to use our framework to provide a unified picture of incentives in the Bitcoin blockchain, for absolute and relative rewards based utility functions, as well as prove novel results regarding incentives of the Fruitchain blockchain protocol [PODC 2017] showing that the equilibrium condition holds for collusions up to $n-1$ players for absolute rewards based utility functions and less than $n/2$ for relative rewards based utility functions, with the latter result holding for any "weakly fair" blockchain protocol, a new property that we introduce and may be of independent interest.