Combinator dynamics: multi-dimensional evolutionary learning

Srinivas Arigapudi (), Omer Edhan (), Yuval Heller () and Ziv Hellman ()
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Srinivas Arigapudi: Department of Economic Sciences, Indian Institute of Technology Kanpur
Omer Edhan: Department of Economics, The University of Manchester
Yuval Heller: Department of Economics, Bar Ilan University
Ziv Hellman: Department of Economics, Bar Ilan University

Theoretical Economics, Forthcoming

Abstract: 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.

Keywords: Multi-dimensional reasoning; non-monotone dynamics; evolutionary stability; imitation (search for similar items in EconPapers)
JEL-codes: C73 D83 L20 (search for similar items in EconPapers)
Date: 2026-06-26
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