2020 Working Paper (2020-02)

Working Paper No. 2020-02
Bandit with Similarity Information
Benjamin Radoc

Abstract 
In problem situations, it is unlikely that a decision maker possesses knowledge on all states of the world so that use of information gathered from past similar experience is plausible. This analogical thinking is formalised by case-based decision theory (CBDT) which suggests that under uncertainty, a decision maker acts based on her memory of past actions and the associated outcomes in past similar situations. A unique experimental setting that makes similarity information in the problem situation salient was created, while providing a fair chance for either Bayesian or case-based decisions to emerge. Consider a two-armed bandit with similarity information. If the similarity cue offers irrelevant information on the payoff distribution of the two arms, it is easy for a Bayesian decision maker to ignore the cue and recognise that the distribution of payoffs of the two arms are identical. But if the similarity cue triggers a decision maker to perceive the two arms as separate, there are two possibilities: (i) more frequent positive payoffs on one arm may be used to put a higher valuation on a similar arm consistent with the prediction of CBDT, or (ii) given past positive payoffs on one arm, the other arm may be valued lower if the subsequent likelihood of success is perceived as lower. The experiment results suggest that although participants in general correctly updated their expectation of a positive payoff based on past experience, the pattern in the decisions shows that participants systematically used the irrelevant similarity cue in a manner that cannot be explained by CBDT but consistent with the gambler’s fallacy or the biased belief that the pattern of past outcomes will reverse.

Keywords: Bayesian reasoning, case-based decisions, gambler’s fallacy, expectation, similarity