  Peer prediction refers to a collection of mechanisms for eliciting
information from human agents when direct verification of the obtained
information is unavailable. They are designed to have a game-theoretic
equilibrium where everyone reveals their private information truthfully. This
result holds under the assumption that agents are Bayesian and they each adopt
a fixed strategy across all tasks. Human agents however are observed in many
domains to exhibit learning behavior in sequential settings. In this paper, we
explore the dynamics of sequential peer prediction mechanisms when participants
are learning agents. We first show that the notion of no regret alone for the
agents' learning algorithms cannot guarantee convergence to the truthful
strategy. We then focus on a family of learning algorithms where strategy
updates only depend on agents' cumulative rewards and prove that agents'
strategies in the popular Correlated Agreement (CA) mechanism converge to
truthful reporting when they use algorithms from this family. This family of
algorithms is not necessarily no-regret, but includes several familiar
no-regret learning algorithms (e.g multiplicative weight update and Follow the
Perturbed Leader) as special cases. Simulation of several algorithms in this
family as well as the $\epsilon$-greedy algorithm, which is outside of this
family, shows convergence to the truthful strategy in the CA mechanism.
