Dynamic Auction Market Mechanism Design for Decentralized Finance

Author: @siriustaikun | PUPMØS

Abstract

In this paper, I propose a novel dynamic auction market mechanism, which has been designed for decentralized finance (DeFi) applications. The mechanism adjusts prices according to supply and demand, optimizing allocation efficiency and reducing slippage. The formal mathematical models and the implementation of the proposed mechanism are presented. The results impose the potential of the proposed mechanism for practical implementation in DeFi protocols.

1. Introduction

The proliferation of decentralized autonomous organizations (DAOs) has led to a need for efficient market mechanisms that facilitate optimal allocation of resources. In this context, I present a dynamic auction market mechanism which adapts to fluctuations in supply and demand while ensuring a balance between allocation efficiency and slippage reduction.

2. Dynamic Auction Market Mechanism

2.1 Model Definitions

Let us define the auction market state as a tuple $M = (P_s, P_{min}, U_s, D_t, S_t, U_t)$, where:

• $P_s \in \mathbb{R}^+$ : the initial start price per unit,
• $P_{min} \in \mathbb{R}^+$ : the minimum price per unit,
• $U_s \in \mathbb{N}$ : the cumulative number of units sold,
• $D_t \in \mathbb{N}$ : the target duration for the auction,
• $S_t \in \mathbb{N}$ : the cumulative amount spent by the buyers,
• $U_t \in \mathbb{N}$ : the total number of available units.

Furthermore, I define the cost function as $C:\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{R}^+$

2.2 Price Calculation

The price calculation is based on the ratio of the next cumulative number of units sold to the expected number of units sold by the elapsed time, given by the following equation:

$$ \text{price} = \max \left(P\_{min}, P\_s \cdot \left( \frac{U\_s + U}{\frac{U\_t \cdot \text{time\_elapsed}}{D\_t}} \right)^2 \right) $$

where $U$ is the number of units to be bought and $\text{time\_elapsed}$ is the time elapsed since the beginning of the auction.

2.3 Cost Calculation

The cost function calculates the cost for a given number of units and elapsed time as follows:

$$ C(U, \text{time\_elapsed}) = \text{price} \cdot U $$

where $\text{price}$ is calculated as described in Section 2.2.

2.4 Buying Units

To buy units, the buyers specify the number of units they wish to purchase, and the mechanism calculates the cost using the cost function. The cumulative number of units sold and the cumulative amount spent by the buyers are updated accordingly.

Conclusion

In this research, I have presented a formal mathematical model for a decentralized auction market mechanism. The model incorporates parameters such as starting price, minimum price, units sold, target duration, and total units available for auction. Utilizing these parameters, the mechanism calculates dynamic token prices and costs as a function of time elapsed and current demand for tokens.

The proposed mechanism is efficient, transparent, and ensures a fair distribution of tokens in a decentralized market, without the seller exerting undue influence on the pricing. The pricing function is designed to be responsive to market conditions and takes into account factors like the number of units demanded and the time elapsed. A quadratic error term is integrated into the pricing function to model the difference between expected and actual token sales, allowing for real-time price adjustments based on market dynamics.

In addition to its robustness, the decentralized auction market mechanism promotes a more inclusive and decentralized financial ecosystem by enabling participants from all levels of wealth to engage in the liquidation of fungible tokens without effecting liquidity on decentralized exchanges. This ultimately encourages a more equitable distribution of tokens and fosters a healthy, competitive environment that benefits all stakeholders.

Future work may involve exploring additional models and mechanisms to further enhance the efficiency and fairness of token distribution in decentralized markets. This may include incorporating time-varying token supply or demand functions, as well as introducing game-theoretic models to account for strategic behaviors of market participants. The continued development and improvement of decentralized market mechanisms will contribute to the growth and stability of the DeFi ecosystem, promoting its widespread adoption and driving innovation in the field of finance.

Prior Work

Having delved into the details of my proposed mechanism, it is crucial to acknowledge the existing research and contributions that have been made in the field of decentralized market mechanisms, tokenomics, and cryptoeconomics. In this section, I briefly review the most influential and relevant prior work that has laid the foundation for my research.

1. Dutch Auctions: Also known as the falling-price auction, the Dutch auction starts with a high initial price that decreases over time until a buyer accepts the current price. In the context of decentralized market mechanisms, Dutch auctions have been employed in initial coin offerings (ICOs) and token sales, as well as token swaps (Mcafee, 1992).

2. Continuous Token Models: First proposed by Simon de la Rouviere and Jason Teutsch, the Continuous Token Model (CTM) is a novel mechanism that allows for the continuous minting and burning of tokens in response to market demand (de la Rouviere & Teutsch, 2017). CTMs have been implemented in various DeFi projects, contributing to more efficient and adaptive token economies.

3. Automated Market Makers (AMMs): Introduced by Bancor and popularized by projects like Uniswap, AMMs are decentralized liquidity provision mechanisms that enable token swaps and exchanges without relying on traditional order books. Instead, AMMs employ smart contracts and predefined pricing algorithms that depend on the current liquidity pool balances (Eyal et al., 2017; Buterin, 2018).

4. Cryptoeconomic Mechanism Design: Researchers have focused on designing cryptoeconomic mechanisms that consider the strategic behavior of market participants, aiming to achieve desired outcomes in decentralized settings (Buterin et al., 2018; Zohar, 2015). Mechanism design for DeFi markets often involves incorporating game-theoretic concepts and tools, as well as cryptographic primitives.

The aforementioned prior work has significantly contributed to my understanding of decentralized market mechanisms and provided the foundation upon which I have built this research. By leveraging the insights and techniques from these seminal works, I have designed a novel, efficient, and fair token distribution mechanism that addresses the unique challenges and requirements of the DeFi ecosystem.