Aggregation of amyloid-β (Aβ) peptides is a significant event that underpins Alzheimer’s disease (AD). Aβ aggregates, especially the low-molecular weight oligomers, are the primary toxic agents in AD pathogenesis. Therefore, there is increasing interest in understanding their formation and behaviour. In this paper, we use our previously established results on heterotypic interactions between Aβ and fatty acids (FAs) to investigate off-pathway aggregation under the control of FA concentrations to develop a mathematical framework that captures the mechanism. Our framework to define and simulate the competing on- and off-pathways of Aβ aggregation is based on the principles of game theory. Together with detailed simulations and biophysical experiments, our models describe the dynamics involved in the mechanisms of Aβ aggregation in the presence of FAs to adopt multiple pathways. Specifically, our reduced-order computations indicate that the emergence of off- or on-pathway aggregates are tightly controlled by a narrow set of rate constants, and one could alter such parameters to populate a particular oligomeric species. These models agree with the detailed simulations and experimental data on using FA as a heterotypic partner to modulate the temporal parameters. Predicting spatio-temporal landscape along competing pathways for a given heterotypic partner such as lipids is a first step towards simulating scenarios in which the generation of specific ‘conformer strains’ of Aβ could be predicted. This approach could be significant in deciphering the mechanisms of amyloid aggregation and strain generation, which are ubiquitously observed in many neurodegenerative diseases.