Some mathematical aspects of DAG-based distributed Ledger systems

Abstract

\n In the first part of this work, we present, model and analyze a randomized automated peering model, that can be implemented to any distributed system. We conclude that the scheme has some desirable properties (specifically, a reasonable message overhead, a reasonable distribution of the numbers of peers of a node, and a negligible probability of an attack by a malicious actor to be successful). In the second part, we present an article published in the volume 136 of the journal Computers & Industrial Engineering, in October of 2019 (DOI 10.1016=j.cie.2019.07.025). In the paper, we analyze the Nash Equilibria of a graph attachment game, defined to represent the different strategies that malicious actors can use to take certain advantages in a DAG-based (i.e., based on Directed Acyclic Graphs) distributed ledger system. We prove the existence of almost symmetric Nash equilibria for the system where a part of players tries to optimize their attachment strategies and another part follows a default one. We also present simulations that show that the selfish players will not choose strategies that are considerably different that the recommended one.\n