Reasoning in Dynamic Games: From Rationality to Rationalization

Rineke Verbrugge 
Department of Artificial Intelligence 
Bernoulli Institute, University of Groningen


ABSTRACT:
Game theorists have proposed backward induction as the reasoning procedure that rational players follow in dynamic games, on the basis of their collective belief that all participating players are rational. An alternative reasoning procedure is forward induction, in which a player rationalizes any previous apparently irrational move by the opponent. Do people's choices in centipede-like dynamic games fit better with backward or forward induction?

In our experiments (with Sujata Ghosh, Aviad Heifetz, and Harmen de Weerd), participants played a centipede-like game called Marble Drop. The computer opponent was programmed to surprise the participant by deviating often from its backward induction strategy at the beginning of the game. Participants had been told that the computer was optimizing against some belief about the participant's future strategy.

In the aggregate, participants tended to favor the forward induction choice. However, their verbalized strategies usually depended on other features, such as risk aversion, trust or cooperativeness. In a follow-up experiment we compared participants from India, Israel and The Netherlands in the Marble Drop game, with surprising results.