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Single-token vs Two-token Blockchain Tokenomics

Aggelos Kiayias, Philip Lazos, Paolo Penna

TL;DR

The approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria and reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy.

Abstract

We study long-term equilibria that arise in the token monetary policy, or tokenomics, design of proof-of-stake (PoS) blockchain systems that engage utility maximizing users and validators. Validators are system maintainers who get rewarded with tokens for performing the work necessary for the system to function properly, while users compete and pay with such tokens for getting a desired portion of the system service. We study how the system service provision and suitable rewards schemes together can lead to equilibria with the following desirable characteristics (1) viability: the system keeps parties engaged, (2) decentralization and skin-in-the-game: multiple sufficiently invested validators are participating, (3) stability: the price path of the underlying token used to transact with the system does not change widely over time, and (4) feasibility: the mechanism is easy to implement as a smart contract, e.g., it does not require a fiat reserve on-chain to perform token {\em buybacks} or to perform bookkeeping of exponentially growing token holdings. Our analysis enables us to put forward a novel generic mechanism for blockchain monetary policy that we call quantitative rewarding (QR). We investigate how to implement QR in single-token and two-token proof of stake (PoS) blockchain systems. The latter are systems that utilize one token for the users to pay the transaction fees and a different token for the validators to participate in the PoS protocol and get rewarded. Our approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria. Our analysis also reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy - a distinction that is, to the best of our knowledge, highlighted for the first time.

Single-token vs Two-token Blockchain Tokenomics

TL;DR

The approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria and reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy.

Abstract

We study long-term equilibria that arise in the token monetary policy, or tokenomics, design of proof-of-stake (PoS) blockchain systems that engage utility maximizing users and validators. Validators are system maintainers who get rewarded with tokens for performing the work necessary for the system to function properly, while users compete and pay with such tokens for getting a desired portion of the system service. We study how the system service provision and suitable rewards schemes together can lead to equilibria with the following desirable characteristics (1) viability: the system keeps parties engaged, (2) decentralization and skin-in-the-game: multiple sufficiently invested validators are participating, (3) stability: the price path of the underlying token used to transact with the system does not change widely over time, and (4) feasibility: the mechanism is easy to implement as a smart contract, e.g., it does not require a fiat reserve on-chain to perform token {\em buybacks} or to perform bookkeeping of exponentially growing token holdings. Our analysis enables us to put forward a novel generic mechanism for blockchain monetary policy that we call quantitative rewarding (QR). We investigate how to implement QR in single-token and two-token proof of stake (PoS) blockchain systems. The latter are systems that utilize one token for the users to pay the transaction fees and a different token for the validators to participate in the PoS protocol and get rewarded. Our approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria. Our analysis also reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy - a distinction that is, to the best of our knowledge, highlighted for the first time.
Paper Structure (39 sections, 12 theorems, 59 equations, 7 figures)

This paper contains 39 sections, 12 theorems, 59 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Main contributions
  3. Model description and notation (single token)
  4. Notation (single token model)
  5. Subround I (pay & stake):
  6. Subround II (buy or sell):
  7. Single token mechanisms
  8. Analysis of price path
  9. Generic symmetric equilibria
  10. The implications of no buybacks and Quantative Rewarding
  11. Main dilemma: Uncontrolled growth of rewards
  12. Policy that accommodates and implements the stable price equilibrium
  13. Given parameters and constraints.
  14. System parameters.
  15. Assumption.
  16. ...and 24 more sections

Key Result

Lemma 1

In any symmetric equilibrium, it holds that Moreover Hence, if $\mathcal{R}^{(t)} \neq 1$, then $u_i^{(t)} = \mathbb{TK}_U^{(t)}$ and $b_i^{(t)}=\mathbb{TK}_U^{(t+1)}$ for all users $i$, and the following identity must hold:

Figures (7)

  • Figure 1: Notation and symbols.
  • Figure 2: The effect of service values on rewards growth when no buyback condition: a small service value (left) can trigger an exponential increase in both rewards and validators staked amounts, while a slightly bigger service value (right) can remove this growth.
  • Figure 3: A too high initial rewards (left) causes an exponential growth, as opposed to a smaller initial rewards (right) leading to stable rewards and staked tokens (note the different scale of the y-axis in the two plots). In both cases, we fix a minimum value of $0.1$ for the rewards, which is the flat part of the green line in the right plot.
  • Figure 4: The effect of risk free rate ($\delta$) on rewards growth when no buyback condition: a smaller $\delta$ might trigger an exponential increase in both rewards and validators staked amounts (compare the right picture here with the right picture in Figure \ref{['fig:impl-stable-const-S']}).
  • Figure 5: The effect of non-stable prices on rewards and validators staked tokens. We set decreasing prices according to the price growth parameter $\delta\mathcal{R}=0.9$. Though the rewards and staked tokens increase exponentially (left) their value expressed in money -- rewards and staked tokens market cap -- does not (right).
  • ...and 2 more figures

Theorems & Definitions (33)

  • Definition 1: symmetric equilibrium
  • Remark 1: viability and equilibria
  • Remark 2: service value fluctuations -- shocks
  • Lemma 1
  • Example 1
  • Remark 3
  • Definition 2: $\gamma$-stable prices
  • Definition 3: generic symmetric equilibrium
  • Theorem 1
  • Corollary 1
  • ...and 23 more