When Can the Weaker Player Win? A Game-Theoretic Model of Humans Against a More Powerful AI

Abstract

As AI systems approach and surpass human ability across more and more tasks, we ask a deliberately pessimistic question: if a far more capable AI turned adversarial, are there still games a human could win, and how? We give a game-theoretic answer. The intuition that “more capable means it wins everything” treats capability as a single number; we instead model it as a seven-component vector: optimization depth, predictive accuracy, observability, action breadth, tempo, commitment, and creativity. A human out-matched on the five computational components can still retain decisive leverage on the remaining two: outright superiority on creativity, the ability to play moves outside the AI’s model of the human, formalized through games with unawareness; and parity on commitment, the ability to move first and bind oneself. We prove that in closed, strictly competitive games enough computation drives the human to the classical security value and creativity is worthless; that creativity has value exactly when an unmodeled move beats the AI’s best defense; that a single inequality decides whether the human is favored; that commitment helps only under partial alignment; and that a creativity advantage is sustainable only if the human innovates faster than the AI’s combined learning-and-consumption rate. Reproducible Monte Carlo simulations numerically corroborate the quantitative results, and we connect the resulting taxonomy of human–AI games to corrigibility and assistance-game designs in AI safety.