game-theory-coalition

Coalition stability analysis checks whether the core exists by verifying that no subset of players can form a profitable blocking coalition. If the core is empty, the proposed allocation faces high defection threats from stakeholders.

Setting up a characteristic function requires defining v(S) to assign a value to every possible subset of players. This function captures the total gain each coalition can achieve through binding agreements and serves as the input for stability and fairness calculations.

The Shapley value does not guarantee a stable coalition formation outcome. It separates what is fair from what is stable; a Shapley allocation can still fall outside the core, meaning blocking coalitions could defect despite the fair division.

The best way to divide alliance budgeting gains is to calculate Shapley marginal contributions for fairness and then verify core stability constraints. This identifies whether the division is stable or highlights the highest-risk defection threats.