Mining blocks on a blockchain equipped with a proof of work consensus protocol is well known to be resource consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining and is compensated by a capital gain when a block is discovered. This paper aims at quantifying the profitability of mining when the possible event of ruin is also considered. This is done by formulating a tractable stochastic model and using tools from applied probability and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when the miner withholds blocks. The obtained explicit expressions allow us to analyze the sensitivity with respect to the different model components and to identify conditions under which selfish mining is a strategic advantage.
Transactive energy plays a key role in the operation and energy management of future power systems. However, the conventional operational mechanism, which follows a centralized design, is often less secure, vulnerable to malicious behaviors, and suffers from privacy leakage. In this work, we introduce blockchain technology in transactive energy to address these challenges. Specifically, we develop a novel blockchain-based transactive energy framework for prosumers and design a decentralized energy trading algorithm that matches the operation of the underlying blockchain system. We prove that the trading algorithm improves the individual benefit and guarantees the socially optimal performance, and thus incentivizes prosumers to join the transactive energy platform. Moreover, we evaluate the feasibility of the transactive energy platform throughout the implementation of a small-scale network of Internet of Things (IoT) devices and extensive simulations using real-world data. Our results show that this blockchain-based transactive energy platform is feasible in practice, and the decentralized trading algorithm reduces the user's individual cost by up to 77% and lowers the overall cost by 24%.
A key performance metric in blockchains is the latency between when a transaction is broadcast and when it is confirmed (the so-called, confirmation latency). While improvements in consensus techniques can lead to lower confirmation latency, a fundamental lower bound on confirmation latency is the propagation latency of messages through the underlying peer-to-peer (p2p) network (inBitcoin, the propagation latency is several tens of seconds). The de facto p2p protocol used by Bitcoin and other blockchains is based on random connectivity: each node connects to a random subset of nodes. The induced p2p network topology can be highly suboptimal since it neglects geographical distance, differences in bandwidth, hash-power and computational abilities across peers. We present Perigee, a decentralized algorithm that automatically learns an efficient p2p topology tuned to the aforementioned network heterogeneities, purely based on peers' interactions with their neighbors. Motivated by the literature on the multi-armed bandit problem, Perigee optimally balances the tradeoff between retaining connections to known well-connected neighbors, and exploring new connections to previously-unseen neighbors. Experimental evaluations show that Perigee reduces the latency to broadcast by $33\%$. Lastly Perigee is simple, computationally lightweight, adversary-resistant, and compatible with the selfish interests of peers, making it an attractive p2p protocol for blockchains.
Samin Aref, Ly Dinh, Rezvaneh Rezapour, Jana Diesner
Balance theory explains the forces behind the structure of social systems, which are commonly modeled as static undirected signed networks. We expand this modeling approach to incorporate directionality of edges, and consider three levels of analysis: triads, subgroups, and the whole network. For triad-level balance, we operationalize a new measure by utilizing semicycles that satisfy the condition of transitivity. For subgroup-level balance, we propose measures of cohesiveness (intra-group solidarity) and divisiveness (inter-group antagonism) to capture balance within and among subgroups of the network using the most fitting partition of nodes into two groups. For network-level balance, we re-purpose the normalized line index to incorporate directionality, and provide the proportion of edges whose position suits balance. Through extensive computational analysis, we quantify and analyze patterns of social structure in triads, subgroups, and the whole network across a range of social settings from college students and Wikipedia editors to philosophers and Bitcoin traders. We then apply our multilevel framework of analysis to examine balance in temporal and multilayer networks, which demonstrates the generalizability of our approach to evaluating balance, and leads to new observations on balance with respect to time and layer dimensions. Our complementary findings on a variety of social networks highlight the need to evaluate balance at different levels. We propose a comprehensive yet parsimonious approach to address this need.
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in particular, any risk neutral distribution can be interpreted as a certificate establishing that no arbitrage exists. We are interested in the case when there are multiple risk-neutral probabilities. We describe a number of convex optimization problems over the convex set of risk neutral price probabilities. These include computation of bounds on the cumulative distribution, VaR, CVaR, and other quantities, over the set of risk-neutral probabilities. After discretizing the underlying price, these problems become finite dimensional convex or quasiconvex optimization problems, and therefore are tractable. We illustrate our approach using real options and futures pricing data for the S&P 500 index and Bitcoin.
Automated market makers, first popularized by Hanson's logarithmic market scoring rule (or LMSR) for prediction markets, have become important building blocks, called 'primitives,' for decentralized finance. A particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers (or CFMMs) which includes existing popular market makers such as Uniswap, Balancer, and Curve, whose yearly transaction volume totals to billions of dollars. We give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset and that they can do so in a computationally efficient way. We also derive several other useful properties that were previously not known. These include lower bounds on the total value of assets held by CFMMs and lower bounds guaranteeing that no agent can, by any set of trades, drain the reserves of assets held by a given CFMM.
We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, and increased wealth heterogeneity over time, or a “rich get richer” effect. This concentration phenomenon is aggravated by a higher Bitcoin mining reward and reduced by competition. Additionally, an advantaged miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium, unaffected by competition from less efficient miners. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies. This paper was accepted by Kay Giesecke, finance. Funding: A. M. Reppen is partly supported by the Swiss National Science Foundation [Grant SNF 181815]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4798 .
In this paper, we consider the problem of generating fair randomness in a deterministic, multi-agent context (for instance, a decentralised game built on a blockchain). The existing state-of-the-art approaches are either susceptible to manipulation if the stakes are high enough, or they are not generally applicable (specifically for massive game worlds as opposed to games between a small set of players). We propose a novel method based on game theory: By allowing agents to bet on the outcomes of random events against the miners (who are ultimately responsible for the randomness), we are able to align the incentives so that the distribution of random events is skewed only slightly even if miners are trying to maximise their profit and engage in block withholding to cheat in games.
This paper presents a stochastic model for block arrival times based on the difficulty retargeting rule used in Bitcoin, as well as other proof-of-work blockchains. Unlike some previous work, this paper explicitly models the difficulty target as a random variable which is a function of the previous block arrival times and affecting the block times in the next retargeting period. An explicit marginal distribution is derived for the time between successive blocks (the blocktime), while allowing for randomly changing difficulty. This paper also aims to serve as an introduction to Bitcoin and proof-of-work blockchains for the controls community, focusing on the difficulty retargeting procedure used in Bitcoin.
This paper deals with the design of the secure blockchain network framework to prevent damages from an attacker. The decentralized network design called the Blockchain Governance Game is a new hybrid theoretical model and it provides the stochastic game framework to find best strategies towards preparation for preventing a network malfunction by an attacker. Analytically tractable results are obtained by using the fluctuation theory and the mixed strategy game theory. These results enable to predict the moment for operations and deliver the optimal portion of backup nodes to protect the blockchain network. This research helps for whom considers the initial coin offering or launching new blockchain based services with enhancing the security features.
We consider users which may have renewable energy harvesting devices, or distributed generators. Such users can behave as consumer or producer (hence, we denote them as prosumers) at different time instances. A prosumer may sell the energy to other prosumers in exchange of money. We consider a demand response model, where the price of conventional energy depends on the total demand of all the prosumers at a certain time. A prosumer depending on its own utility has to select the amount of energy it wants to buy either from the grid or from other prosumers, or the amount of excess energy it wants to sell to other prosumers. However, the strategy, and the payoff of a prosumer inherently depends on the strategy of other prosumers as a prosumer can only buy if the other prosumers are willing to sell. We formulate the problem as a coupled constrained game, and seek to obtain the generalized Nash equilibrium. We show that the game is a concave potential game and show that there exists a unique generalized Nash equilibrium. We consider that a platform will set the price for distributed interchange of energy among the prosumers in order to minimize the consumption of the conventional energy. We propose a distributed algorithm where the platform sets a price to each prosumer, and then each prosumer at a certain time only optimizes its own payoff. The prosumer then updates the price depending on the supply and demand for each prosumer. We show that the algorithm converges to an optimal generalized Nash equilibrium. The distributed algorithm also provides an optimal price for the exchange market.
Crowdsourcing relies on people's contributions to meet product- or system-level objectives. Crowdsourcing-based methods have been implemented in various cyber-physical systems and realtime markets. This paper explores a framework for Crowdsourced Energy Systems (CES), where small-scale energy generation or energy trading is crowdsourced from distributed energy resources, electric vehicles, and shapable loads. The merits/pillars of energy crowdsourcing are discussed. Then, an operational model for CESs in distribution networks with different types of crowdsourcees is proposed. The model yields a market equilibrium depicting traditional and distributed generator and load setpoints. Given these setpoints, crowdsourcing incentives are designed to steer crowdsourcees to the equilibrium. As the number of crowdsourcees and energy trading transactions scales up, a secure energy trading platform is required. To that end, the presented framework is integrated with a lightweight Blockchain implementation and smart contracts. Numerical tests are provided to showcase the overall implementation.
We are proposing two greedy and a new linear programming based approximation algorithm for the total positive influence dominating set problem in weighted networks. Applications of this problem in weighted settings include finding: a minimum cost set of nodes to broadcast a message in social networks, such that each node has majority of neighbours broadcasting that message; a maximum trusted set in bitcoin network; an optimal set of hosts when running distributed apps etc. Extensive experiments on different generated and real networks highlight advantages and potential issues for each algorithm.