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

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.