cryptocurrency network operators

Abstract: The goal of this paper is to distill insight around the trade-offs present on Bayesian equilibria of transaction fee mechanism (TFM) design under $n$ multiple concurrent proposers (MCP). We conceptualize a technical toolkit that unlocks the analysis of hard-to-characterize equilibria of finite Bayesian MCP TFM games by examining sequences of joint user--proposer mixed equilibria as the number of users increases and keeping the relative congestion $ρ$ that they cause fixed in the sequence limit. We first consider the popular mechanisms of "pay-once" (which charges transactions its bid only once regardless of the duplicate copies that end up being included by proposers) and "pay-per-inclusion" (PPI in short, which charges a transaction for each copy that appears). We prove that PPI is efficient in the limit of equilibria sequences, and incentivizes users to route to only one proposer. We characterize $m$ users' asymptotic behavior in PPI even in finite markets varying with $O(\sqrt{m})$, where we show users in a $Θ(n\sqrt{ρ(1-ρ)/m})$ window near an efficient cutoff exhibit fixed inclusion probability akin to a normal distribution's CDF. We additionally show that on a value-dependent basis, pay-once exhibits a higher degree of duplication and lower probability of inclusion for higher-value transactions than PPI. Pay-once's inefficiency persists even in the large market limit and even in regimes with ample blockspace where all transactions fit across all blocks. We study interpolations between these two mechanisms proving that some higher coefficients (towards PPI) reduce duplication and increase inclusion probability. We then use our tools to show that exclusive proposer payments yield inefficient equilibria (in fact, with maximal possible duplication), even if users still pay multiple times when included more than once and their payment is burnt when non-exclusive.

Abstract: The global structure of P2P networks underlying modern cryptocurrencies is hidden by design: each node only knows its neighbors and maintains a local \textit{peer table} of IP addresses. The peer table of a node can be seen as the node's ``local view'' of the set of nodes currently in the network: it is constantly updated with information collected from the neighbors and it is used by the node to establish new connections when needed. The maintenance rules of the nodes' peer tables determine the global structure of the network and its evolution. Even though the global structure is unknown to any node of the network as well as to any external observer, the rules for the exchange of information between neighbors are compatible with the design and use of network \textit{crawlers} that can query the nodes and extract some information about their peer tables. In this paper we first analyze the data we crawled from nodes of the Bitcoin and Dogecoin P2P networks, to collect information about the distribution of IP addresses in the peer tables and to estimate the evolution of network size and churn rate; we then use the estimates to set up the parameters for a simulation of the Bitcoin network and we analyze the evolution of the network structure that we get from the simulation. Overall, our results show that Bitcoin's peer-table maintenance rules induce non-uniform, heavy-tailed visibility patterns while nevertheless generating a well-connected and structurally robust network.