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Blockchain networks have attracted tremendous attention for creating cryptocurrencies and decentralized economies built on peer-to-peer protocols. However, the complex nature of the dynamics and feedback mechanisms within these economic networks has rendered it difficult to reason about the growth and evolution of these networks. Hence, proper mathematical frameworks to model and analyze the behavior of blockchain-enabled networks are essential. To address this need, we establish a formal mathematical framework, based on dynamical systems, to model the core concepts in blockchain-enabled economies. Drawing on concepts from differential games, control engineering, and stochastic dynamical systems, this paper proposes a methodology to model, simulate, and engineer networked token economies. To illustrate our framework, a model of a generalized token economy is developed, where miners provide a commodity service to a platform in exchange for a cryptocurrency and users consume a service from the platform. We illustrate the dynamics of token economies by simulating and testing two different block reward strategies. We then conclude by outlining future research directions that will integrate additional methods from signal processing and control theory into the toolkit for designers of blockchain-enabled economic systems.

This interdisciplinary paper blends knowledge from computer science and economics in proposing a complex dynamic system subpopulation model for a blockchain form of local complementary currency, generic to the Grassroots Economics Foundation’s Community Inclusion Currency (CIC) implemented in Kenya. Our contribution to the emerging economics literature is five-fold: (i) we take a novel meso-economic approach to elicit utility from actual transactions data and reveal an ‘optimal’ disaggregation number of typical community subgroups; (ii) we relate the local CIC functioning to a nation-wide currency board monetary regime to argue that such a credible CIC implementation ensures trust in the CIC and makes it a valuable market-based channel to alleviate poverty, in addition to humanitarian or government aid channels. However, (iii) we also find evidence in our data that substitutes for real-world money such as CICs are perceived as inferior, and hence CIC systems can only be transitional. Then, (iv) we reveal that, for a poor population, saving dominates as a use of a cluster’s CIC balance, accounting for 47%, followed by purchase of food and water, 25%. Despite these dominant patterns, (v) we uncover a considerable heterogeneity in CIC spending behavior. Our contribution to the related computer-science and Tokenomics literature is two-fold: (i) we provide an open-source scaffold for modeling CIC viability and net flows; (ii) to simulate a subpopulation mixing process, we employ a network-based dynamical system modeling approach that is better grounded in economic principles and monetary theory.

Many challenges in network science and engineering today arise from systems composed of many individual agents interacting over a network. Such problems range from humans interacting with each other in social networks to computers processing and exchanging information over wired or wireless networks. In any application where information is spread out spatially, solutions must address information aggregation in addition to the decision process itself. Intelligently addressing the trade off between information aggregation and decision accuracy is fundamental to finding solutions quickly and accurately. Network optimization challenges such as these have generated a lot of interest in distributed optimization methods. The field of distributed optimization deals with iterative methods which perform calculations using locally available information. Early methods such as subgradient descent suffer very slow convergence rates because the underlying optimization method is a first order method. My work addresses problems in the area of network optimization and control with an emphasis on accelerating the rate of convergence by using a faster underlying optimization method. In the case of convex network flow optimization, the problem is transformed to the dual domain, moving the equality constraints which guarantee flow conservation into the objective. The Newton direction can be computed locally by using a consensus iteration to solve a Poisson equation, but this requires a lot of communication between neighboring nodes. Accelerated Dual Descent (ADD) is an approximate Newton method, which significantly reduces the communication requirement. Defining a stochastic version of the convex network flow problem with edge capacities yields a problem equivalent to the queue stability problem studied in the backpressure literature. Accelerated Backpressure (ABP) is developed to solve the queue stabilization problem. A queue reduction method is introduced by merging ideas from integral control and momentum based optimization.

In the first of three works we consider a generalized dynamical system (GDS) extended from that initially proposed by [25, 24], where a data structure is mapped to itself and the space of such mappings is closed under composition. We argue that GDS is the natural environment to consider questions arising from the computational implementation of autonomous and semi-autonomous decision problems with one or more constraints, nesting into one framework well-studied models of optimal control, system dynamics, agent-based modeling, and networks, among others. Particular attention is paid to mathematical constructions which support applications in mechanism design. The contingent derivative approach is defined, along with an associated metric, for which a GDS admits the study of existence of state trajectories that satisfy system constraints. The system may also be interpreted as a discretized version of a differential inclusion, allowing the characterization of the reachable subspaces of the state space, and locally controllable trajectories. The second and third parts in the three-part series are briefly described and cover, respectively, applications and implementations, with the latter demonstrating explicitly how a GDS can be implemented as software using Complex Adaptive Dynamics Computer Aided Design (cadCAD) [30].

This paper examines the potential for Cyber-Physical Systems (CPS) to be governed in a decentralised manner, whereby blockchain-based infrastructure facilitates the communication between digital and physical domains through self-governing and self-organising principles. Decentralised governance paradigms that integrate computation in physical domains (such as 'Decentralised Autonomous Organisations' (DAOs)) represent a novel approach to autono-mous governance and operations. These have been described as akin to cybernetic systems. Through the lens of a case study of an autonomous cabin called \"no1s1\" which demonstrates self-ownership via blockchain-based control and feedback loops, this research explores the potential for blockchain infrastructure to be utilised in the management of physical systems. By highlighting the considerations and challenges of decentralised governance in managing autonomous physical spaces, the study reveals that autonomy in the governance of autonomous CPS is not merely a technological feat but also involves a complex mesh of functional and social dynamics. These findings underscore the importance of developing continuous feedback loops and adaptive governance frameworks within decentralised CPS to address both expected and emergent challenges. This investigation contributes to the fields of infra-structure studies and Cyber-Physical Systems engineering. It also contributes to the discourse on decentralised governance and autonomous management of physical spaces by offering both practical insights and providing a framework for future research.

Blockchain networks and similar cryptoeconomic networks are systems, specifically complex systems. They are adaptive networks with multiscale spatio-temporal dynamics. Individual actions may be incentivized towards a collective goal with “purpose-driven” tokens. Blockchain networks, for example, are equipped cryptoeconomic mechanisms that allow the decentralized network to simultaneously maintain a universal state layer, support peer-to-peer settlement, and incentivize collective action. These networks represent an institutional infrastructure upon which socioeconomic collaboration is facilitated – in the absence of intermediaries or traditional organizations. They provide a mission-critical and safety-critical regulatory infrastructure for autonomous agents in untrusted economic networks. Their tokens provide a rich, real-time data set reflecting all economic activities in their systems. Advances in network science and data science can thus be leveraged to design and analyze these economic systems in a manner consistent with the best practices of modern systems engineering. Research that reflects all aspects of these socioeconomic networks needs (i) a complex systems approach, (ii) interdisciplinary research, and (iii) a combination of economic and engineering methods, here referred to as “economic systems engineering,” for the regulation and control of these socioeconomic systems. This manuscript provides a conceptual framework synthesizing the research space and proceeds to outline specific research questions and methodologies for future research in this field, applying an inductive approach based on interdisciplinary literature review and relative contextualization of the works cited.

This paper proposes a complex dynamic systems subpopulation model for the construction and validation of a novel form of local complementary currency, namely the Grassroots Economics Foundation's Community Inclusion Currency (CIC) implemented recently in Kenya. Differently from other related work in computer science or of a legal nature, we frame our analysis in a deeper economic context, thus bridging the gap across these parallel literatures. First, we highlight the potential usefulness of the emerging blockchain-technology backed CICs, now popular in the new - and interdisciplinary - field of cryptoeconomics. Essentially, CICs can act as a local liquidity-provision institutional device in poor or isolated economic regions to increase their internal exchange and economic value added, thereby serving as a market-based mechanism to alleviate poverty, in addition to government aid and akin in its automatism and credibility to a currency board monetary regime in national economies. The ultimate goal of these CIC systems is to promote a transition toward complete inclusion and integration into the national and global economies, pulling over the communities and regions out of self-sufficiency and poverty into more advanced stages of economic development and well-being. Second, we elicit 50 heterogeneous utility types according to observed transactions behavior and build a corresponding model and simulation at a meso-economic level, which for many purposes could prove more insightful for policymakers than the usual extreme perspectives of micro and macro.

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.

Decentralized Ledger Technology, popularized by the Bitcoin network, aims to keep track of a ledger of valid transactions between agents of a virtual economy without a central institution for coordination. In order to keep track of a faithful and accurate list of transactions, the ledger is broadcast and replicated across machines in a peer-to-peer network. To enforce validity of transactions in the ledger (i.e., no negative balance or double spending), the network as a whole coordinates to accept or reject new transactions based on a set of rules aiming to detect and block operations of malicious agents (i.e., Byzantine attacks). Consensus protocols are particularly important to coordinate operation of the network, since they are used to reconcile potentially conflicting versions of the ledger. Regardless of architecture and consensus mechanism used, resulting economic networks remain largely similar, with economic agents driven by incentives under a set of rules. Due to the intense activity in this area, proper mathematical frameworks to model and analyze behavior of blockchain-enabled systems are essential. In this paper, we address this need and provide the following contributions: (i) we establish a formal framework, with tools from dynamical systems theory, to mathematically describe core concepts in blockchain-enabled networks, (ii) we apply this framework to the Bitcoin network and recover its key properties, and (iii) we connect our modeling framework with powerful tools from control engineering, such as Lyapunov-like functions, to properly engineer economic systems with provable properties. Apart from the aforementioned contributions, the mathematical framework herein proposed lays a foundation for engineering more general economic systems built on emerging Turing complete networks, such as the Ethereum network, through which complex alternative economic models are explored.

The study of how to set up cryptocurrency incentive mechanisms and to operationalize governance is token economics. Given the $250 billion market cap for cryptocurrencies, there is compelling need to investigate this topic. In this paper, we present facets of the token engineering process for a real-life 80-person Swiss blockchain startup, Insolar. We show how Insolar used systems modeling and simulation combined with cryptocurrency expertise to design a mechanism to incentivize enterprises and individual users to use their new MainNet public blockchain network. The study showed subsidy pools that incentivize application developers to develop on the network does indeed have the desired positive effect on MainNet adoption. For a startup like Insolar whose success hinge upon how well their model incentivizes various stakeholders to participate on their MainNet network versus that of numerous alternatives, this token economics simulation analysis provides invaluable insights.