Abstract

How does the ability to opt out affect learning in sequential games? We design a modified version of the Game of 21 (G21) where players can drop out at any time similar to the centipede game, referred to as C21, to answer this query. Motivating our study with two reinforcement learning models when players have limited foresight, we explore if players learn to backward induce more after ten rounds of C21 compared to G21. To compare the amount of learning between C21 and G21 with a more precise measure of foresight, the experiment introduces the novel concept of a “dumb computer” that makes suboptimal decisions. Players learn better when forced to finish, the G21 treatment. Additional complexity, strategic uncertainty, and a subset of players using the opt-out option to “give up” by opting out non-strategically are likely the reasons of more learning in G21 compared to C21.