Combinator Dynamics: Multi-Dimensional Evolutionary Learning

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 actions dimension by dimension, imitate successful traits in each dimension, and then combine the selected traits into a new action. We analyse key properties of these dynamics – monotonicity, stationarity, and stability. We then extend the model to heterogeneous settings, where some players imitate entire multi-dimensional actions while others combine traits imitated separately in each dimension. We apply the framework to organisational decision-making, where decentralised adoption of practices can generate coordination failures, persistent performance differences, and a trade-off between specialised and versatile organisational traits.

Keywords: non-monotone dynamics, evolutionary stability JEL codes: C73, multi-dimensional reasoning, imitation

JEL Classification: C73, D83, L20