Additive valuation ($v_i(S)={\sum }_{j\in S}{v}_{ij}$)

A bundle-value function for which an agent's value for a set of items is the sum of its item values. Different agents may assign different values to the same item. With nonnegative item values, a bundle containing no positively valued item has value zero. The formula excludes interactions such as a pair of items being valuable only when held together.