4 products targeted towards college students. Consider one of the ideas from our student generated pool: Convertible High-Heel Shoe: Many prefer high-heel shoes for dress-up occasions, yet walking in high heels for more than short distances is very challenging. Might we create a stylish high-heel shoe that easily adapts to a comfortable walking configuration, say by folding down or removing a heel portion of the shoe? In this example, the unmet need is the desire of some people to dress-up and wear high-heel shoes while at other times using the same shoes to comfortably walk longer distances. The proposed solution is to make the heel portion of the shoe in a way that it can be folded down or removed. Note that at this abstract level of a short verbal description the value of the idea is highly uncertain. We can think of uncertain value as a random variable that is drawn from an underlying pay-off distribution. The realization of this random pay-off will require further investments, with each investment resolving some of the uncertainty. Market research and prototypes are two common forms of investment to reduce uncertainty for new products. The realized value of the pay-off is only observed after the idea is introduced into the market. There exists a very large number of possible new product ideas that differ along many dimensions. In other words, we can think of ideas as positions in a highly dimensional space. Each idea in this space has an unknown value associated with it. For the sake of illustration, consider an idea space with only two dimensions. Each idea thus corresponds to a (x, y) coordinate in the graph. The vertical dimension (z-axis) can be thought of as the expected value of the idea. This is illustrated by Figure 1.