Artificial Intelligence and Strategic Uncertainty: Can AI Play Mixed Strategies?

Abstract

Numerous decision making tasks require humans to engage in strategic uncertainty where game theory predicts they should adopt a mixed strategy. While past research calls into question this ability in humans, I ask whether artificial intelligence is able to play mixed strategies appropriately. I have it interact in a two-player, 2x2 zero-sum game where the opponent takes a fixed, pre-selected strategy. I devise three tests of optimal behavior. First, I show that AI does not play mixed strategies appropriately in that the empirical frequency of play does not match equilibrium predictions when playing against an opponent who is playing the equilibrium strategy. Second, it exhibits positive serial correlation in its play. In addition, I include treatments where its opponent exhibits either perfect negative serial correlation or perfect positive serial correlation. Given positive serial correlation in its play, in games where AI's opponent also exhibits positive serial correlation AI does well, but when playing against an opponent exhibiting negative serial correlation its earnings tend to be negative. Third, I extend the game to consider two additional treatments where in one AI's payoff is reduced in one cell of the game matrix and another treatment where its opponent's payoff increases. While Nash equilibrium predicts AI's behavior will respond to changes in its opponent's payoff and not adjust behavior when its payoff changes, I show that AI does the opposite. Taken together, AI is unable to engage in strategic uncertainty.

Keywords: artificial intelligence, ChatGPT, Minimax Hypothesis, mixed strategy, Robinson Crusoe Fallacy, serial correlation, strategic uncertainty

JEL Classification: D90, C72