Belief and higher‐order belief in the centipede games: An experimental investigation

Abstract

This paper experimentally explores epistemic conditions behind the subgame perfect equilibrium (SPNE) of centipede games. We propose a novel design of laboratory experiment to elicit subjects’ beliefs regarding their opponents’ strategies and 1st-order beliefs. The measured beliefs, together with the choice data, help us to estimate each subject’s level of rationality, belief of rationality, and 2nd-order belief of rationality. We consider two experimental treatments: the classic centipede game in which an efficient non-equilibrium outcome exists, and its constant-sum variation. Data shows that, in the classic centipede treatment, fewer subjects behave rationally; meanwhile, subjects are less likely to believe in their opponents’ rationality and belief of rationality. Furthermore, in the constant-sum centipede treatment, there is a non-trivial portion of subjects who behave rationally, believe in others’ rationality, and hold 2nd-order belief of rationality. Our results indicate that the efficiency property of the classic centipede game may lead to subjects’ non-equilibrium behavior by diffusing their beliefs and higher-order beliefs.