Humans are able to predict each other’s actions by reasoning about the others’ underlying goals, preferences, and motives, such as greed and risk-aversion. Game theory provides a framework for studying human behaviors through incentivized games that simulate social situations. We utilized two validated games from the cognitive science literature—the Social Prediction Game (SPG) and the Inspection Game (IG)—to systematically study how well several recent open- and closed-source LLMs predict player actions and whether they can leverage and generalize the players’ motives learned from the iterated games. Our results indicate that state-of-the-art LLMs can achieve accuracy close to human levels in predicting players’ actions with underlying human motives in SPGs. However, unlike humans, who rely on reasoning about players’ motives to inform their predictions, LLMs failed to recognize statistical patterns in players’ actions. As a result, LLM prediction accuracy did not improve over multiple rounds. Our results in the IG further demonstrate that, unlike humans, LLMs were unable to recognize a player’s underlying motives and to generalize their understanding of the same player to a new context. This suggests that LLMs may lack reasoning capabilities. Our findings offer insights into differences in human and LLM reasoning mechanisms, suggesting that further research into human-AI alignment is needed before utilizing LLMs for human behavior modeling and simulation in this and related contexts.