A Control Theoretic Approach to Infrastructure-Centric Blockchain Tokenomics Oguzhan Akcin Robert P. Streit Benjamin Oommen

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A Control Theoretic Approach to

Infrastructure-Centric Blockchain Tokenomics

Oguzhan Akcin, Robert P. Streit, Benjamin Oommen,

Sriram Vishwanath, and Sandeep Chinchali

The University of Texas at Austin {oguzhanakcin, rpstreit,

baoommen, sriram, sandeepc}@utexas.edu

Abstract. There are a multitude of Blockchain-based physical infras-

tructure systems, ranging from decentralized 5G wireless to electric ve-

hicle 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. How-

ever, today’s token economies are largely designed without infrastructure

systems in mind, and often operate with a ﬁxed token supply (e.g., Bit-

coin). 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 to-

ken rewards should gracefully scale with the size of the decentralized sys-

tem, 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 adapt-

able and controllable so that it maximizes the total utility of all users,

such as achieving stable (overall non-inﬂationary) token economies.

Our main contribution is to model infrastructure token economies

as dynamical systems – the circulating token supply, price, and con-

sumer demand change as a function of the payment to nodes and costs

to consumers for infrastructure services. Crucially, this dynamical sys-

tems 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 tra-

ditional algorithmic stablecoin heuristics by up to 2.4×in simulations

based on real demand data from existing decentralized wireless networks.

Keywords: Blockchain Token Economics ·Optimal Control Theory ·

Game Theory

1 Introduction

The space of Blockchain-based physical infrastructure networks is rapidly grow-

ing, including decentralized wireless, storage, compute, and electric vehicle charg-

arXiv:2210.12881v1 [cs.DC] 23 Oct 2022

2 O. Akcin et al.

Payment

Controller

Blockchain

Nodes

Token

Payments

Consumer

Demand

Forecast

Dollar +

Token

Reserve

+ 𝑢!

Token Buy-Backs

- 𝑢!

+𝐼𝑛𝑐𝑜𝑚𝑒!State.𝑥!

Network.

Utility.J

“Central” Treasury

Fig. 1: A Control System for

Blockchain Tokenomics: We

design a controller (gray) to

achieve a burn and mint equi-

librium. The controller takes in

a forecast of consumer demand

and supplier growth st, as well

as the treasury state xt. Then,

it adaptively controls token pay-

ments uP

tand buy-backs uB

tto

achieve a stable token price.

ing 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 decen-

tralized ﬁle storage and computing services. These networks reward suppliers

using a corresponding (cryptocurrency) token to build, maintain, secure, and of-

fer 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 sys-

tematic tools to design their token economies to incentivize supply growth and

consumer demand. Today’s token economies largely target ﬁnance, such as Bit-

coin, 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 supply-

demand 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)

A Control Theoretic Approach to Blockchain Tokenomics 3

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 sys-

tems, which allows us to leverage powerful ideas from mathematical control

theory to maximize a Blockchain network’s utility function under chosen con-

straints. 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 econ-

omy. Moreover, we can design a control cost function that captures key metrics

for desired performance and evolution of the Blockchain dynamical system. Cru-

cially, 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.

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 to-

kenomics and introduce a general-purpose dynamical systems model that ﬂex-

ibly 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 con-

trollers, 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 He-

lium 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

4 O. Akcin et al.

demand, and the strength of our controller’s predictions relates with the strength

of the forecasts used in the system.

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 inter-

ests 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).

The state vector is denoted by xt∈Rn, the control vector by ut∈Rm,

and the dynamics are given by xt+1 =f(xt, ut, st), where stis an exogenous

timeseries input, such as a demand forecast. Since we have forecasts of node and

consumer growth for Hsteps in the future, we naturally have a ﬁnite horizon

control problem of Hsteps. Our goal is to optimize the performance metric,

which is to minimize the aggregate control cost J. Typically, the control cost J

is a sum of a terminal cost and stage costs penalizing state deviations from a

reference trajectory (tracking error) and control eﬀort, of the form J=cH(xH)+

PH−1

t=0 ct(xt, ut), where ct(xt, ut)is a possibly time-variant cost.

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

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AControlTheoreticApproachtoInfrastructure-CentricBlockchainTokenomicsOguzhanAkcin,RobertP.Streit,BenjaminOommen,SriramVishwanath,andSandeepChinchaliTheUniversityofTexasatAustin{oguzhanakcin,rpstreit,baoommen,sriram,sandeepc}@utexas.eduAbstract.ThereareamultitudeofBlockchain-basedphysicalinfras-truct...

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A Control Theoretic Approach to Infrastructure-Centric Blockchain Tokenomics Oguzhan Akcin Robert P. Streit Benjamin Oommen

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