Finite-Order Beliefs and Welfare-Enhancing Instruments in the Centipede Game

This paper investigates the effectiveness of two instruments designed to defer termination in the centipede game: an insurance against termination by the opponent, and an option to offer the opponent a bonus for not terminating the game. The rational prediction in both cases is passing until close to the end. Empirically, however, only the bonus option is used by the subjects. The results indicate that subjects readily understand the strategic effect of the bonus, which, once offered, renders passing until close to the end the strictly dominant strategy for both players. Yet, they fail to realise the slightly more involved strategic signal entailed in the insurance, namely that passing until close to the end is a strictly dominant strategy for an insured player. In order to further investigate this effect, we propose a simple behavioural model based on level-k thinking and show that it is largely consistent with the data.