Identifying level-k reasoning in repeated games: Strategies, beliefs, and cognitive ability

788/2026 David Gill, Yaroslav Rosokha

In this paper, we identify level-k reasoning in repeated games that operates at the level of a supergame strategy, rather than at the level of individual rounds. First, we develop a model of level-k reasoning that incorporates choices over strategies as well as beliefs about strategies chosen by others. Then, using data from the Indefinitely Repeated Prisoner's Dilemma that includes elicited strategies and beliefs about strategies, we classify a substantial fraction of subjects as level-1 or level-2. Moreover, we show that when level-k reasoning operates at the level of a strategy, cognitive ability and experience both predict higher level reasoning.

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