Competitive equilibria between staking and on-chain lending (2001.00919v2)

Abstract: Proof of Stake (PoS) is a burgeoning Sybil resistance mechanism that aims to have a digital asset ("token") serve as security collateral in crypto networks. However, PoS has so far eluded a comprehensive threat model that encompasses both Byzantine attacks from distributed systems and financial attacks that arise from the dual usage of the token as a means of payment and a Sybil resistance mechanism. In particular, the existence of derivatives markets makes malicious coordination among validators easier to execute than in Proof of Work systems. We demonstrate that it is also possible for on-chain lending smart contracts to cannibalize network security in PoS systems. When the yield provided by these contracts is more attractive than the inflation rate provided from staking, stakers will tend to remove their staked tokens and lend them out, thus reducing network security. In this paper, we provide a simple stochastic model that describes how rational validators with varying risk preferences react to changes in staking and lending returns. For a particular configuration of this model, we provide a formal proof of a phase transition between equilibria in which tokens are predominantly staked and those in which they are predominantly lent. We further validate this emergent adversarial behavior (e.g. reduced staked token supply) with agent-based simulations that sample transitions under more realistic conditions. Our results illustrate that rational, non-adversarial actors can dramatically reduce PoS network security if block rewards are not calibrated appropriately above the expected yields of on-chain lending.

• The paper introduces a stochastic model that predicts a phase transition between predominant staking and on-chain lending, affecting network security.
• Simulation results show that higher lending yields can prompt stakers to divert funds, potentially triggering a security crisis similar to a bank run.
• The findings emphasize the need for adjusted reward structures in PoS systems, revealing that monetary policies critically influence staking behavior.

Competitive Equilibria between Staking and On-Chain Lending: An Expert Overview

Overview

The paper "Competitive equilibria between staking and on-chain lending" offers an analytical exploration into the dynamics and potential vulnerabilities within Proof-of-Stake (PoS) cryptocurrency networks, specifically focusing on how on-chain lending might pose a threat to network security. As PoS mechanisms become integral to many blockchain networks, understanding the economic incentives and potential risks involved in staking versus lending is critical.

Core Contributions

The primary contribution of this research is the introduction of a stochastic model that captures the behavior of rational validators who allocate capital between staking and on-chain lending, based on their varying risk preferences. This model is designed to show how alternative yields, such as those provided by on-chain lending, impact the allocation of staking tokens, ultimately affecting network security. Notably, the paper provides strong mathematical support and agent-based simulation results to bolster these findings.

Key Results

1. Phase Transition in Stake-Lending Equilibrium: The research outlines a formal proof of a phase transition between equilibria where tokens are mainly staked versus predominantly lent. This suggests that under certain financial conditions, stakers may find lending more attractive, which could drastically reduce network security.
2. Effect of On-Chain Lending Yields: The paper shows a significant relationship between the yields from on-chain lending and staking returns. If lending yields surpass the inflation-adjusted returns from staking, stakers are likely to shift their tokens away from securing the network to obtaining higher yields, leading to a security reduction reminiscent of a bank run.
3. Simulation of Rational Agent Behavior: Through agent-based simulations, the paper demonstrates that rational, non-adversarial participants can inadvertently compromise PoS security. This occurs because they optimize for financial returns rather than network security, especially when staking rewards are not competitive with lending yields.
4. Sensitivity to Monetary Policy: The simulations reveal that PoS systems with deflationary monetary policies are particularly susceptible to security threats from on-chain lending dynamics. In contrast, systems with more inflationary policies might be better insulated from such vulnerabilities.

Implications and Future Directions

The findings have significant implications for the design and sustainability of PoS networks. The research suggests that blockchain networks need to carefully design reward structures that incentivize staking above the yields available through on-chain lending. This entails setting appropriate block rewards that are responsive to the market dynamics created by on-chain financial products.

Theoretically, this work calls for an expanded security model for PoS systems that incorporates economic and financial attack vectors alongside traditional Byzantine fault tolerance models. Practically, the insight gained from this research could guide the development of new protocols and financial regulations within blockchain ecosystems to bolster security against market-driven rational behavior shifts.

Future research could build upon these insights by incorporating more complex economic models and extending the analytical framework to include transaction fees and unbonding periods. Additionally, exploring heterogeneous agent networks where validators have different information sets could provide further depth to the understanding of staking and lending dynamics.

Through its thorough analysis and methodology, this paper lays an intellectual foundation for addressing one of the emerging economic challenges in PoS systems, offering both a cautionary perspective as well as a pathway towards more robust decentralized networks.