A Dynamic Level-k Model in 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, namely limited induction and time unraveling, and helps to resolve paradoxical behaviors in the centipede game, finitely repeated prisoner’s dilemma, and chain store game, three canonical games where backward induction performs poorly. The dynamic level-k model can be considered as a tracing procedure for backward induction because the former converges to the latter in the limit.