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

David Gill and Yaroslav Rosokha

Papers from arXiv.org

Abstract: In this paper, we identify level-$k$ reasoning in repeated games that operates at the level of a supergame strategy. First, we develop a model of level-$k$ reasoning that incorporates choices over strategies as well as beliefs about the strategies chosen by others. Then, jointly using elicited strategies and beliefs about strategies from the indefinitely repeated Prisoner's Dilemma, and applying a new notion of balance-optimal error tolerance, 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 repeated-game strategy, cognitive ability and experience predict higher level reasoning.

Date: 2026-10
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