Combinator dynamics: multi-dimensional evolutionary learning

In complex strategic settings with multiple dimensions, players often simplify de- cisions by breaking them down into separate dimensions. In contrast to standard replicator dynamics, which assume perfect multi-dimensional coordination, our com- binator 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.