Determine Value of Item in Bundle Let's say I construct a series of bundles of different sizes, containing different items, like:
Bundle 1     Bundle 2     Bundle 3
Item A       Item A       Item D
Item B       Item D       Item C
Item C       Item E       Item F
             Item F

And so on.  Each bundle has a "value".  For the sake of this example, let's say the items are things I sell.  I put them into these bundles and then allow people to bid on the bundles, like an auction.  The resulting bid is the "value" of the bundle.
What I'm looking for is a methodology or technique which allows me to untangle the value of the individual items from the value of the bundle.  It seems to me that, with enough bundles data, it should be possible to estimate how much people value each individual item.  But I'm not sure what sort of a problem this is, nor where to start looking for how to solve it.  Can anyone help me out by pointing me in the right direction?
 A: This is a tricky one because bundling certain items together might enhance or reduce an items value compared with that, had they been sold separately. My first approach would be to create a linear model that attempted to predict the value of the bundles ($Y_{n}$) on the basis on their contents. You'll need to treat each item as a dummy variable and include interactions where you suspect combining items enhances or reduces their value. 
Take the following, where $X_{A}$ is a dummy variable for Item A, $X_{i}$ is the $i_{th}$ item, $X_{j}$ is some complimentary item to item i and $Y_{n}$ is the value of the bundle n.
$Y_{n}=\alpha+\beta_{A}X_{A}+\beta_{B}X_{B}+...+ \beta_{i}X_{i}+\beta_{AB}X_{A}X_{B}...+\beta_{ij}X_{i}X_{j}+ \epsilon$
You could hypothesis that the standalone value of Item A is equal to the coefficient $\beta_{A}$, holding for all other items and item interactions (assuming your model accounts for all interactions). 
If in the above $\beta_{AB}$ was statistically significant and positive you would conclude that bundling items A and B together enhances their worth.  You may need to have 3 or even 4 way interactions i.e $...+\beta_{ABC}X_{A}X_{B}X_{C}+...$.
