A Game-Theoretic Model for Co-Adaptive Brain-Machine Interfaces

Co-adaptation in brain-machine interfaces (BMIs) can improve performance and facilitate user learning. We propose and analyze a mathematical model for co-adaptation in BMIs. We model the brain and the decoder as strategic agents who seek to minimize their individual cost functions, leading to a game-theoretic formulation of interaction. We frame our BMI model as a potential game to identify stationary points (Nash equilibria) of the brain-decoder interactions, which correspond to points at which both the brain and the decoder stop adapting. Assuming the brain and the decoder adapt using gradient-based schemes, we analytically show how convergence to these equilibria depends on agent learning rates. This theoretical framework presents a basis for modeling co-adaptation using dynamic game theory and can be extended to tasks with multiple dimensions and to different decoder models. This framework can ultimately be used to develop robust adaptive decoder designs to shape brain learning and optimize BMI performance.