We apply path integral techniques to study the dynamics of agent-based models withasymmetric information structures. In particular, we devise a batch version of a modelproposed originally by Berg et al (2001 Quantitative Finance 1 203), and convert thecoupled multi-agent processes into an effective-agent problem from which the dynamicalorder parameters in ergodic regimes can be derived self-consistently togetherwith the corresponding phase structure. Our dynamical study complements andextends the available static theory. Results are confirmed by numerical simulations.