Bounds of Block Rewards in Honest PinFi Systems

2024-04-01

arXiv.org

AI Summary

PinFi suffers from a threefold stability crisis—LPs prefer external arbitrage, internal selling dominates market-making contributions, and insufficient on-protocol selling willingness—stemming from misaligned LP incentives. Method: We propose the first three-state game-theoretic model of LP behavior, grounded in Nash equilibrium analysis and dynamical systems stability theory. Contribution/Results: We rigorously derive necessary and sufficient conditions for endogenous protocol stability under the honesty assumption, and establish tight upper and lower bounds on block rewards that guarantee long-term stability. Our analysis reveals a non-empty reward interval—achievable under typical parameter settings—that simultaneously curbs external arbitrage, incentivizes sustained market-making, and attains dynamic equilibrium among buyers, sellers, and LPs. This work provides a verifiable theoretical framework and quantitative design principles for mechanism design in decentralized liquidity protocols.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Cryptocurrency and smart contracts
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• Addresses liquidity providers' preference for external market selling over protocol participation
• Examines LPs' tendency to sell within system rather than provide liquidity
• Analyzes scenarios where LPs are unwilling to sell within the protocol

Innovation

• Game-theoretic analysis of PinFi protocol mechanisms
• Dynamic equilibrium among liquidity providers and traders
• Calibrated block reward range ensures system stability