Authors: (1) Oguzhan Akcin, The University of Texas at Austin (oguzhanakcin@utexas.edu); (2) Robert P. Streit, The University of Texas at Austin (rpstreit@utexas.edu); (3) Benjamin Oommen, The University of Texas at Austin (baoommen@utexas.edu); (4) Sriram Vishwanath, The University of Texas at Austin (sriram@utexas.edu); (5) Sandeep Chinchali, The University of Texas at Austin (sandeepc@utexas.edu). Authors: Authors: (1) Oguzhan Akcin, The University of Texas at Austin (oguzhanakcin@utexas.edu); (2) Robert P. Streit, The University of Texas at Austin (rpstreit@utexas.edu); (3) Benjamin Oommen, The University of Texas at Austin (baoommen@utexas.edu); (4) Sriram Vishwanath, The University of Texas at Austin (sriram@utexas.edu); (5) Sandeep Chinchali, The University of Texas at Austin (sandeepc@utexas.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction A Primer on Optimal Control The Token Economy as a Dynamical System Control Design Methodology Strategic Pricing: A Game-Theoretic Analysis Experiments Discussion and Future Work, and References A Primer on Optimal Control A Primer on Optimal Control The Token Economy as a Dynamical System The Token Economy as a Dynamical System Control Design Methodology Control Design Methodology Strategic Pricing: A Game-Theoretic Analysis Strategic Pricing: A Game-Theoretic Analysis Experiments Experiments Discussion and Future Work, and References Discussion and Future Work, and References Abstract. There are a multitude of Blockchain-based physical infrastructure systems, ranging from decentralized 5G wireless to electric vehicle charging networks. These systems operate on a crypto-currency enabled token economy, where node suppliers are rewarded with tokens for enabling, validating, managing and/or securing the system. However, today’s token economies are largely designed without infrastructure systems in mind, and often operate with a fixed token supply (e.g., Bitcoin). Such fixed supply systems often encourage early adopters to hoard valuable tokens, thereby resulting in reduced incentives for new nodes when joining or maintaining the network. This paper argues that token economies for infrastructure networks should be structured differently – they should continually incentivize new suppliers to join the network to provide services and support to the ecosystem. As such, the associated token rewards should gracefully scale with the size of the decentralized system, but should be carefully balanced with consumer demand to manage inflation and be designed to ultimately reach an equilibrium. To achieve such an equilibrium, the decentralized token economy should be adaptable and controllable so that it maximizes the total utility of all users, such as achieving stable (overall non-inflationary) token economies. Abstract Our main contribution is to model infrastructure token economies as dynamical systems – the circulating token supply, price, and consumer demand change as a function of the payment to nodes and costs to consumers for infrastructure services. Crucially, this dynamical systems view enables us to leverage tools from mathematical control theory to optimize the overall decentralized network’s performance. Moreover, our model extends easily to a Stackelberg game between the controller and the nodes, which we use for robust, strategic pricing. In short, we develop predictive, optimization-based controllers that outperform traditional algorithmic stablecoin heuristics by up to 2.4× in simulations based on real demand data from existing decentralized wireless networks. 1 Introduction The space of Blockchain-based physical infrastructure networks is rapidly growing, including decentralized wireless, storage, compute, and electric vehicle chargng networks. As an example, Helium [18] and Pollen [22] are two prominent decentralized wireless networks (DeWi) that reward the general public to build, maintain, validate, secure and ultimately, send data over 5G hotspots. Similarly, projects such as FileCoin [20], Storj [21] and ComputeCoin [27] offer decentralized file storage and computing services. These networks reward suppliers using a corresponding (cryptocurrency) token to build, maintain, secure, and offer services over this decentralized infrastructure network. Likewise, consumers can often exchange US dollars (USD) for tokens, which enables them to utilize infrastructure services and/or participate in the associated crypto-economy. Despite the popularity of decentralized infrastructure networks, we lack systematic tools to design their token economies to incentivize supply growth and consumer demand. Today’s token economies largely target finance, such as Bitcoin, and can operate with a (typically) fixed supply of tokens. However, these fixed supply monetary systems are starkly different from physical infrastructure networks. For example, in a fixed supply system such as Bitcoin, early adopters can hoard tokens since they are scarce. Moreover, late adopters might not be adequately incentivized to join or maintain the network as token rewards could prove to be smaller than those of early participants. Our central thesis is that a token economy must be designed to continually incentivize new suppliers to join the ecosystem and provide services, such as 5G connectivity for Helium or electric vehicle charging stations. As such, the number of tokens should gracefully scale with the size of the infrastructure network, which we do not know a-priori. However, continually rewarding suppliers with newly created tokens can result in inflation if such payments are not carefully balanced with the consumer demand for infrastructure services. To solve such problems, a number of projects have recently considered adopting/adopted a “burn-and-mint” token economics (tokenomics) model, where a central reserve “mints” tokens to reward suppliers, while tokens are “burnt” (deleted from the circulating supply) when consumers want to use network services. By adaptively burning tokens, we can reduce the token supply to reach an overall supplydemand equilibrium. Moreover, such a burn-and-mint equilibrium (BME) [1] must be “programmable” so that Blockchain-based infrastructure networks can maximize the total utility of all users. For example, this network utility function (performance criterion) can include maintaining a stable, steadily growing token price with low volatility. Likewise, this network cost function can incentivize new suppliers/consumers to expand geographical coverage. Moreover, the BME-based token economy could be designed to satisfy strict performance guarantees and constraints, such as limiting the number of tokens minted and/or burned per day. Taking this even further, participants in the economy are likely rational and so it is important to consider their agency – and any impacts – in taking actions to maximize the value of their holdings. In short, solutions deployed in infrastructure-centric Blockchain networks must address these aspects in their design when managing token supply. Our key insight is that token economies can be modeled as dynamical systems, which allows us to leverage powerful ideas from mathematical control theory to maximize a Blockchain network’s utility function under chosen constraints. Control theory is a natural tool since the token economy is a dynamical system – the circulating token supply, token price, and consumer demand change as a function of our burn and mint decisions. Likewise, we have control authority – we are able to adapt the burn or mint mechanisms to regulate the token economy. Moreover, we can design a control cost function that captures key metrics for desired performance and evolution of the Blockchain dynamical system. Crucially, we can model the dynamics of the system, since we engineer the Blockchain protocol and token economy dynamics. As such, regulating the Blockchain token economy is a model-based control problem, which can be solved using powerful ideas from nonlinear optimization and optimal control theory. mathematical control theory Overall, the contributions of this paper are three-fold. To the best of our knowledge, we are the first to apply optimal control theory to Blockchain tokenomics and introduce a general-purpose dynamical systems model that flexibly captures both fixed-supply as well as burn-and-mint systems. We design a control system for a token economy using nonlinear model predictive control (MPC) methods that are used in high-performance, safety-critical applications like autonomous driving [34,7], robotic manipulation, and rocket guidance [4]. We demonstrate that these methods perform better than common heuristic controllers, such as proportional integral derivative (PID) controllers used by some algorithmic stablecoins. Specifically, we improve on PID by 2.4× on simulated timeseries demand patterns and by 2.7× on real demand patterns from the Helium DeWi Blockchain. Finally, we introduce a novel game-theoretic formulation for how owners of tokens and a central reserve strategically interact to maximize network welfare. Related Work: Generally, prior research on Blockchains as dynamical sytems [35,36,10] focus on miner profitability and on the influence of Block rewards on supply and demand dynamics. Our work differs from existing literature in that we focus on understanding incentives and equilibrium in infrastructure-centric Blockchain systems. Specifically, in our case, the supply is fully specified by the actions of the controller, while the demand is specified via forecasts. Thus, our controller specification is decoupled from the possibly complex trajectory of the demand, and the strength of our controller’s predictions relates with the strength of the forecasts used in the system. Related Work In order to better understand the robustness of our methodology, we also consider the impact of rational behavior on the part of the consumers in our system. To achieve this, game theoretic analyses in Blockchain systems have been used over many years, starting with the original Bitcoin whitepaper [26]. Since the discovery of the selfish mining attack [16], game theoretic methods have been used to investigate rational deviations [12], mining pools [15], and more recently transaction fee auctions in Ethereum like Blockchains [31,13]. Our work differs from existing literature as we focus on the effects of rational behavior on buy-back and pay strategies used to stabilize token prices, and not necessarily on modeling the effects on an underlying Blockchain protocol. Finally, as our aim is to stabilize a token price in a Blockchain network, our work bears a degree of similarity to algorithmic stable-coins. However, our interests are in intelligently controlling the circulating supply of a token to balance payments to service providers needed to scale a network with a pre-specified control trajectory on the token price. Thus, our work is more related to service networks employing burn and mint systems such as Helium [18] (which inspired our model) and Factom [32] than more general purpose stable-coins like Reflexer [2] or Terra [19]. Furthermore, most existing literature is reactive through the use of heuristic methods such as PID, whereas our work is predictive through optimal adaptive control methods. As our focus is on infrastructure networks, our work is applicable to DeWi [24] scenarios like Helium [18], as well as file sharing [20] and decentralized video streaming [30]. 2 A Primer on Optimal Control We now provide a basic primer on optimal control theory, which enables us to naturally model the token economy as a controlled dynamical system. Using this, we describe the state of a dynamical system, the control inputs, dynamics, and the high-level performance criterion (cost function). Crucially, we have a good nominal model of the dynamics, since the token economy is under our design. Of course, there are uncertainties which arise due to the stochastic demand forecast st. Since we have known nominal dynamics, we use standard model-based control techniques, which solve an optimization problem to find the optimal set of controls to minimize the cost function subject to dynamics constraints [11,9]. Moreover, we often constrain the state xt and control ut to lie in sets X and U respectively to capture, for example, strict actuation limits. Thus, the general optimal control problem can be stated as: This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv
