SHAP-decide: a cooperative game theory approach to model and solve multiple criteria decision-making problems
本文提出用合作博弈中的Shapley值求解多准则决策问题，将每个备选方案视为博弈中的玩家，通过决策矩阵计算联盟值，并引入OWA-Shapley方法实现从专家到共识导向的灵活决策，在三个实际案例中验证了其高效性和可解释性。
This paper demonstrates how cooperative game theory, especially the Shapley value, can be applied to solve multiple criteria decision-making (MCDM) problems. Each alternative is modelled as a player in a transferable-utility game, with coalition values derived from the decision matrix. An alternative’s priority is determined by its Shapley value, which reflects its expected marginal contribution. It is shown that coalition functions obtained from column-wise maximum aggregation form a class of simple monotone games whose Shapley values can be expressed in a closed form similar to the classical airport-game formula. This results in an exact rank–tail decomposition: for each criterion, sorted scores and level differences are accumulated using analytically defined layer weights, producing Shapley values in O(m * n log n) time without enumerating coalitions. To capture both specialist and compromise behaviour, we introduce ordered weighted averaging (OWA)–Shapley, which replaces the maximum layer with an OWA using a top-k geometric-tail formulation. The parameters k and λ control the transition from specialist to consensus-oriented aggregation. The methodology is evaluated on three real-world cases with 10, 24, and 50 alternatives and compared to several established MCDM methods. Results indicate that OWA–Shapley provides exact, interpretable, and computationally efficient rankings, with tuneable decision behaviour and strong empirical consistency.