  This paper presents a study of the Poof-of-Stake (PoW) Ethereum consensus
protocol, following the recent switch from Proof-of-Work (PoS) to
Proof-of-Stake within Merge upgrade. The new protocol has resulted in reduced
energy consumption and a shift in economic incentives, but it has also
introduced new threat sources such as chain reorganizations and balancing
attacks. Using a simple and flexible agent-based model, this study employs a
time-continuous simulation algorithm to analyze the evolution of the blocktree
and assess the impact of initial conditions on consensus quality. The model
simulates validator node behavior and the information propagation throughout
the peer-to-peer network of validators to analyze the resulting blockchain
structure. Key variables in the model include the topology of the peer-to-peer
network and average block and attestation latencies. Metrics to evaluate
consensus quality are established, and means to observe the model's
responsiveness to changes in parameters are provided. The simulations reveal a
phase transition in which the system switches from a consensus state to a
non-consensus state, with a theoretical justification presented for this
observation.
