  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.
