Equilibria in the Tangle

TL;DR

This paper analyzes the Tangle, a DAG-based stochastic process used in IOTA, proving the existence of near-symmetric Nash equilibria and showing through simulations that selfish players tend to cooperate with the network.

Contribution

It introduces a game-theoretic analysis of the Tangle, demonstrating equilibrium existence and the tendency of rational players to adopt cooperative strategies.

Findings

Existence of almost symmetric Nash equilibria in the Tangle model

Selfish players tend to cooperate by choosing strategies similar to the recommended one

Simulations support the theoretical findings of cooperative behavior

Abstract

We analyse the Tangle --- a DAG-valued stochastic process where new vertices get attached to the graph at Poissonian times, and the attachment's locations are chosen by means of random walks on that graph. These new vertices, also thought of as "transactions", are issued by many players (which are the nodes of the network), independently. The main application of this model is that it is used as a base for the IOTA cryptocurrency system (www.iota.org). We prove existence of "almost symmetric" Nash equilibria for the system where a part of players tries to optimize their attachment strategies. Then, we also present simulations that show that the "selfish" players will nevertheless cooperate with the network by choosing attachment strategies that are similar to the "recommended" one.