Stable Experimentation? An Analysis of Multi-Armed Bandit Problems with Bundling

This paper introduces bundled experimentation problems and compares behavior in these problems to a classic (non-bundled) experimentation problem. We transform a two-decision four-armed bandit problem into two different bundling experimentation problems. The first bundling problem is a “stable” problem where each type of urn in the four-armed bandit problem becomes bundled with a known urn of the same quality. The second bundling problem is an “encouraged” problem where the urn types with larger exploration incentives in the four-armed bandit get bundled with urns with higher known reward rates. In our experiment, there should be no differences in the (expected) information generated from the first decision in each type of experimentation problem. However, we find that both types of bundling problems lead to more expected information generated than the non-bundled experimentation problem. Additionally, in contrast to theory, we find that subjects’ second decision in a bundled bandit problem is influenced by the balls drawn from both of the initially chosen options urns. These two results suggest that choice is not preserved when transforming a non-bundled experimentation problem into a bundled experimentation problem.