A Dynamic Level-k Model in Centipede Games

Backward induction is the most widely accepted principle for predicting behavior in dynamic games. In experiments, however, players frequently violate this principle. An alternative is a 2-parameter “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 past plays to improve their guesses. The model captures two systematic violations of backward induction in the centipede game, limited induction and time unraveling. The dynamic level-k model can be considered as a tracing procedure for backward induction because the former always converges to the latter in the limit.