Equilibria in the tangle

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 [1]. 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.1 this refers to the well-known relation between reversible Markov chains and electric networks, see e.g. the classical book [7] 2 we also cite [2,3,17,22] which deal with other approaches to using DAGs as distributed ledgers 3 that is, the underlying graph is essentially Z + (after discarding finite forks)

When Internet of Things Meets Blockchain: Challenges in Distributed Consensus

“…In [12], the authors analyze the speed of the cumulative weight typically grow in the stationary high load regime, it provides some qualitative and quantitative insights into the consensus process of the Tangle. In [14], the authors prove the existence of ("almost symmetric") Nash equilibria in a DAG-valued stochastic process where a part of players try to optimize their strategies. Considering the features of consensus process, we believe that an analytical model using Markov chain is a promising approach.…”

Spatial Positioning Token (SPToken) for Smart Mobility

“…Our interest in IOTA stems from the fact that its architecture is designed to facilitate high-frequency microtrading. In particular, the architecture places a low computational and energy burden on devices using IOTA, it is highly scalable, there are no transaction fees, and transactions are pseudo-anonymous [26]. In terms of mobility applications, we note that several DLT architectures have already been proposed.…”

“…In other words, in a DAG there is no directed path that connects a vertex with itself. The IOTA Tangle is a particular instance of a DAG-based DLT [26], where each vertex or site represents a transaction, and where the graph, with its topology, represents the ledger. Whenever a new vertex is added to the Tangle, this must approve a number of previous transactions (normally two).…”

“…This process ensures that vehicles have to be physically in the interested locations to be able to issue transactions. This further authentication step makes SPToken a permissioned Tangle (similar to permissioned blockchains [27]), i.e., a DAG-based distributed ledger where a certain amount of trusted nodes (the observers, in this case) is responsible to maintain the consistency of the ledger (as opposed to a public one, where security is handled by a cooperative consensus mechanism [26]).…”

G-IOTA: Fair and confidence aware tangle

“…Strategies to maintain an IOTA-tagle have been proposed and analyzed in [6]. IOTA-tangle properties have been formalized and analyzed in [2], [7] and [4]. More recently, [10] and [1] analyze in detail the stability and the attack resilience of IOTA-tangle.…”