A Dynamic Level-k Model in Sequential Games
提出动态层级-k模型，通过规则层级和基于历史的选择，解释蜈蚣博弈和序贯讨价还价博弈中逆向归纳的系统性偏离，并证明该模型随重复进行收敛于逆向归纳。
Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the “centipede game,” however, players frequently violate this principle. An alternative is a “dynamic level-k” model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level-k rule is a best response to the level-(k-1) rule, and the level-∞ rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level-k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level-k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.