  We relax the strong rationality assumption for the agents in the paradigmatic
Kyle model of price formation, thereby reconciling the framework of
asymmetrically informed traders with the Adaptive Market Hypothesis, where
agents use inductive rather than deductive reasoning. Building on these ideas,
we propose a stylised model able to account parsimoniously for a rich
phenomenology, ranging from excess volatility to volatility clustering. While
characterising the excess-volatility dynamics, we provide a microfoundation for
GARCH models. Volatility clustering is shown to be related to the self-excited
dynamics induced by traders' behaviour, and does not rely on clustered
fundamental innovations. Finally, we propose an extension to account for the
fragile dynamics exhibited by real markets during flash crashes.
