Game theory studies the interactions among agents that try to maximize their payoffs by choosing from a set of actions. When this interaction occurs over time, the agents can change their choice of action depending on what they believe is the best action at any given time. This process constitutes a learning mechanism and can be described by various dynamical systems. Different dynamical systems arise as a result of different forms of belief update.

We focus on two classic learning mechanisms: replicator dynamics (RD) and best-response dynamics (BRD). It is known that the Nash equilibria, describing the outcome of the game, are the same for these two learning mechanisms. However, even when the Nash equilibrium is locally stable its basins of attraction for RD and BRD can be very different. In such cases, the learning outcome can be distinct depending on the learning mechanism and no prediction about the game's outcome can be made. We provide sufficient conditions that guarantee a considerable intersection of the basins of attraction, including full coincidence. These conditions depend on the indifference of the agents with respect to the available actions.