We propose a method for modelling economic systems in which outcomes depend locally on the predictions that agents make of other agents. We develop populations games in which each agent adaptively searches for a good model of its environment. We demonstrate that such systems can exhibit persistent dynamics, cyclic oscillations between low and high complexity states, and other complex, yet endogenous, phenomena. We propose that these `adaptively rational' agents as a natural extension of rational expectations, suitable when mutual consistency is not realistic. We discuss the connections between our work and the programs of bounded rationality, evolutionary game theory, and models motivated by statistical mechanics.
