1. Learning-in-game (LiG) systems are of clear applicational interest (e.g. internet economics). It deviates from the standard ML regime, since these systems are dynamical with continuing prediction-decision interactions (feedback loop) between algorithms and human.
2. In general, a game can have multiple Nash equilibria with vastly different qualities. It is unclear which equilibrium is the "expected" outcome; perhaps, none of them.
3. But the issue does not exist for two-player zero-sum game, as John von Neumann's Minimax theorem guarantees essentially unique solution to such game.
4. Zero-sum game is naturally associated to minimax problem. This has ML applications in adversarial learning, most notably, GAN.
5. The above two points gave us some hope that standard optimization methods might be capable to "learn" or converge to equilibrium of two-player zero-sum games. But the reality is crueler than what we hoped for --- using natural and popular online optimization algorithms turns out to be chaotic.
6. (Local) convergence can be guaranteed in some specific settings, by using ideas in optimization theory and dynamical systems.