Bounds of Block Rewards in Honest PinFi Systems

TL;DR

This work tackles stability in PinFi, a decentralized pricing protocol for dissipative assets, by modeling the market as a game among LPs, speculating sellers, speculating buyers, and genuine buyers under an honesty assumption. It adopts a quasi-static, constant-product AMM framework to derive governing dynamics, cessation times, and profit relations, yielding explicit bounds on block rewards $\gamma$ and on pricing parameters ($\alpha$, $\beta$, $\delta$, $\theta$) that support equilibria among participant roles. Key contributions include closed-form expressions for arbitrage-driven dynamics, a phase-diagram analysis that identifies a balanced region $aG$ in parameter space, and concrete gamma and alpha bounds that calibrate incentives to retain LPs while mitigating arbitrate risk. The findings offer a principled parameterization for sustaining PinFi’s long-term utility and fair pricing, with future work aimed at validating the theory via Monte Carlo and on-chain simulations and extending the model to richer interaction patterns.

Abstract

PinFi is a class of novel protocols for decentralized pricing of dissipative assets, whose value naturally declines over time. Central to the protocol's functionality and its market efficiency is the role of liquidity providers (LPs). This study addresses critical stability and sustainability challenges within the protocol, namely: the propensity of LPs to prefer selling in external markets over participation in the protocol; a similar inclination towards selling within the PinFi system rather than contributing as LPs; and a scenario where LPs are disinclined to sell within the protocol. Employing a game-theoretic approach, we explore PinFi's mechanisms and its broader ramifications. Our findings reveal that, under a variety of common conditions and with an assumption of participant integrity, PinFi is capable of fostering a dynamic equilibrium among LPs, sellers, and buyers. This balance is maintained through a carefully calibrated range of block rewards for LPs, ensuring the protocol's long-term stability and utility.

Figures (4)

• Figure 1: The dynamics of the PinFi system are explored through (a) a general framework and (b) a framework assuming honesty among participants. In (c), participants are categorized by their economic motivations: speculating sellers, speculating buyers, genuine buyers, and liquidity providers.
• Figure 2: The dynamics between the SSs and LPs.
• Figure 3: The dynamics between liquidity providers and the (a) speculating buyers and (b) genuine buyers.
• Figure 4: Phase Diagrams Illustrating the Dynamics and Equilibria in Dissipative Asset Pricing: Panels (a) through (c) showcase variations in the parameter $C = \frac{\theta-\delta}{\beta+p\theta}$, with values set at 0.7, 1.0, and 1.3, respectively, to depict different pricing dynamics. The diagrams incorporate constant parameters $A = \frac{\beta}{\beta+p\theta} = 0.3$ and $B = \frac{p\theta-\delta}{\beta+p\theta} = 0.7$, facilitating comparisons across scenarios. Panel (d) mirrors the configuration of panel (c) but further delineates the diagram into distinct zones, labeled aA through aG, for detailed analysis. Panel (e) provides a detailed zoom-in view of zone aG from panel (d), highlighting the intricate dynamics within this specific region.