Impossibility of $n-1$-strong-equllibrium for Distributed Consensus with Rational Agents

TL;DR

This paper proves the impossibility of achieving $n-1$-strong equilibrium in distributed consensus with rational agents for even numbers of agents, and characterizes the unique solutions for odd numbers, including a $n-2$-strong equilibrium in rings.

Contribution

It establishes the impossibility results for $n-1$-strong equilibrium in all topologies with rational agents and identifies the unique algorithm solutions for odd $n$, including a $n-2$-strong equilibrium.

Findings

Impossibility of $n-1$-strong equilibrium for even $n$ in all topologies.

Uniqueness of Afek et al.'s algorithm for odd $n$.

Existence of a $n-2$-strong equilibrium in synchronous rings for even $n$.

Abstract

An algorithm for $n-1$-strong-equillibrium for distributed consensus in a ring with rational agents was proposed by Afek et al. (2014). A proof of impossibility of $n-1$-strong-equillibrium for distributed consensus in every topology with rational agents, when $n$ is even, is presented. Furthermore, we show that the algorithm proposed by Afek et al. is the only algorithm which can solve the problem when $n$ is odd. Finally, we prove that the proposed algorithm provides a $n-2$-strong-equillibrium in a synchronous ring when $n$ is even.