An Evolutionary Approach to Multi-Dimensional Learning with Application to Firms

Abstract

In complex strategic settings with multiple dimensions, players often simplify decisions by breaking them down into separate dimensions. In contrast to standard replicator dynamics, which assume perfect multi-dimensional coordination, our combinator dynamics model captures cases in which players revise decisions separately in each dimension. We analyse key properties of this dynamic – monotonicity, stationarity, and stability – highlighting its divergence from replicator dynamics. We apply the new dynamics to decision-making in firms, where it is common for divisions to handle different aspects of complex multi-dimensional strategies. We illustrate via examples coordination challenges and persistent performance differences among firms. We then extend the model to heterogeneous settings, where some players imitate entire multi-dimensional strategies while others combine traits imitated separately in each dimension.

Keywords: non-monotone dynamics, evolutionary stability JEL codes: C73, multi-dimensional reasoning, persistent performance differences

JEL Classification: C73, D83, L20