The reference chapter can be found in this book.

Shapley Values (SV) explain prediction via considering each feature as a player and prediction as the payout and deals with how to fairly distribute the payout among the players
has solid base in coalitional game theory
gain (payout) here is the difference between actual prediction and average
SV for an instance is the average marginal contribution of a feature value across all possible coalitions (weighted average, to be precise)
marginal contribution = difference between prediction with and without this feature value
computing SV for linear models is very straightforward
SV satisfy the following properties
- Efficiency - feature contributions add upto difference between predicted and mean prediction
- Symmetry - SV of 2 feature values should be the same if they contribute equally for all coalitions
- Dummy - if a feature value does not contribute to the output, then its value should be 0
- Additivity - for ensemble models, final SV can be computed by adding up the individual SV from each of the underlying models

$$\phi_j = \sum_{S \subset {x} - {x_j}} \frac{len(S)! (p - len(S) - 1)!}{p!} (val(S \bigcup {x_j}) - val(S))$$

$$val(S) = \int_{x \notin S} f(x_1, ..., x_p) - E[f(X)]$$

Where:

$$\phi'j = \frac{1}{M} \sum{m=1}^M f(x_{+j}^m) - f(x_{-j}^m)$$

Where:

$$M$$ - number of samples
$$f(x_{+j}^m)$$ - prediction where the feature values are first randomly permuted and then the first j feature values are kept from the input sample while the rest are randomly picked from another sample in the dataset.
$$f(x_{-j}^m)$$ - same as above but with j-th feature value also chosen at random from another sample

suffers from inclusion of unrealistic feature values
computationally super expensive
explanation involves all the features, which can be difficult for humans to further interpret, as opposed to explainer models like LIME.