  Beliefs inform the behavior of forward-thinking agents in complex
environments. Recently, sequential Bayesian inference has emerged as a
mechanism to study belief formation among agents adapting to dynamical
conditions. However, we lack critical theory to explain how preferences evolve
in cases of simple agent interactions. In this paper, we derive a Gaussian,
pairwise agent interaction model to study how preferences converge when driven
by observation of each other's behaviors. We show that the dynamics of
convergence resemble an Ornstein-Uhlenbeck process, a common model in
nonequilibrium stochastic dynamics. Using standard analytical and computational
techniques, we find that the hyperprior magnitudes, representing the learning
time, determine the convergence value and the asymptotic entropy of the
preferences across pairs of agents. We also show that the dynamical variance in
preferences is characterized by a relaxation time $t^\star$, and compute its
asymptotic upper bound. This formulation enhances the existing toolkit for
modeling stochastic, interactive agents by formalizing leading theories in
learning theory, and builds towards more comprehensive models of open problems
in principal-agent and market theory.
