Competitive equilibria between staking and on-chain lending

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.

Improved Price Oracles: Constant Function Market Makers

“…The increase in usage and participation in automated market makers has led to a vast set of new scoring rules and pricing mechanisms. Analyzing these mechanisms, which range from LMSR style market makers and CFMMs to scoring rules for rates [12], from the perspective of optimization provides insight into why certain mechanisms are more popular than others. In particular, we generalize the results of [5] to demonstrate that CFMMs provide an easy optimization problem for arbitrageurs to synchronize off-chain and on-chain pricing data.…”

“…where λ ∈ R + is the Lagrange multiplier for the inequality constraint of (10), and ∆ , Λ are optimal for (10). Since we wish to look at the marginal price after the no-arbitrage trade, we then set Π = Λ 1, which would then imply that Λ and ∆ are also optimal for (12). (This is easy to see: note that the objective of (10) depends only on Λ1, so constraining Λ1 to be equal to Λ 1, a constant, yields the claim.…”

SoK: Lending Pools in Decentralized Finance

“…Lending pool behaviour at the user level is modelled in [48], which simulates agents interacting with the Compound implementation to examine the evolution of liquidatable and undercollateralized debt, notions similar to (strong) ε-collateralization safety (12) (14). [39,40] examine the competition for user deposits between staking in proof-of-stake systems and lending pools: in the case where lending pools are believed to be more profitable, users may shift deposits away from the staking contract of the underlying consensus protocol towards lending pools, thereby endangering the security of the system.…”

“…As a matter of fact, a recent failure of the oracle price feed used by the Compound lending pool platform led to $100M of collateral being (incorrectly) liquidated [19]. Indeed, most current literature in DeFi is devoted to study the economic impact of these incentive mechanisms [39,40,[46][47][48]50].…”