Procedural Rationality, Asset Heterogeneity and Market Selection

We extend the model of Anufriev and Bottazzi (2010) to the case with many assets. We show that under the procedural equilibrium, all assets with nonzero aggregate demand must have the same price returns. Heterogeneity in price returns appears when some assets face zero demand. In this case, the returns are essentially driven by the matrix of wealth-weighted products between demands and they generate a rich variety of patterns for agents' market shares. We formalize the dynamics of deterministic skeletons in our market model and consider the associated Jacobian matrix, for which we provide a closed form expression up to a matrix inversion. We then introduce the characteristic ratio of an investment strategy, which involves the average dividend yields of the risky assets and the investors' portfolio compositions. When equilibrium returns are uniform and when the number of assets is not smaller than the number of agents, the equilibrium with a single survivor can only be stable if the survivor has the maximal characteristic ratio. Moreover, we prove that this stability criterion holds as long as the noise in the system is sufficiently small. We confirm all our findings with a thorough empirical analysis of numerical simulations, with and without noise. All in all, our results form a theoretical rationale for portfolio strategies tilted towards firms that pay high dividend yields