A reinforcement learning process in extensive form games

The CPR (“cumulative proportional reinforcement”) learning rule stipulates that an agent chooses a move with a probability proportional to the cumulative payoff she obtained in the past with that move. Previously considered for strategies in normal form games (Laslier, Topol and Walliser, Games and Econ. Behav., 2001), the CPR rule is here adapted for actions in perfect information extensive form games. The paper shows that the action-based CPR process converges with probability one to the (unique) subgame perfect equilibrium.Received: October 2004