The serious games between humans and AI have only just begun. Evolutionary Game Theory (EGT) models the competitive and cooperative strategies of biological entities. EGT could help predict the potential evolutionary equilibrium of humans and AI. The objective of this work was to examine EGT models relevant to human-AI interaction, evolution, and co-evolution. Of thirteen EGT models considered, three were examined: the Hawk-Dove Game, Iterated Prisoner's Dilemma, and the War of Attrition. This selection was based on the widespread acceptance and clear relevance of these models to potential human-AI evolutionary dynamics and co-evolutionary trajectories. The Hawk-Dove Game predicts balanced mixed-strategy equilibria based on the costs of conflict. Iterated Prisoner's Dilemma suggests that repeated interaction may lead to cognitive co-evolution. The War of Attrition suggests that competition for resources may result in strategic co-evolution, asymmetric equilibria, and conventions on sharing resources. Each model was examined from the perspective of human and AI decision-making, from psychological and biological perspectives, and from an AI viewpoint. AI is being shaped by human input and is evolving in response to it. So too, neuroplasticity allows the human brain to evolve in response to stimuli. If humans and AI converge in future, what might be the result of human neuroplasticity combined with an ever-evolving AI? There are profound ethical and cognitive implications. EGT may provide a suitable framework to understand and predict human-AI interaction, evolution, and co-evolution. However, future research should extend beyond EGT and explore additional frameworks, empirical validation methods, and interdisciplinary perspectives. In the spirit of further exploration, an illustrative computational simulation is provided.

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