We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote process. We characterize the impact of changing the quota (i.e., the minimum number of seats in the parliament that are required to form a coalition) on the...

This paper defines a class of cooperative fuzzy games with infinite players, which is monotonically nondecreasing and continuous with respect to each player’s grade of membership. Then, the AumannShapley values for the games with fuzzy coalitions are proposed with the form of Choquet integral. The properties of the Aumann-Shapley values are also shown. Finally, the relationship between the fuzz...

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lowervalue based method to associate coalitional games ...

The exact linear dependency among age, period and birth cohort makes it impossible to recover the true parameters of Age-Period-Cohort (APC) models. We then propose extract reliable information from APC models via Shapley decomposition, a model-agnostic procedure game theory that allows pin down most likely contribution each regressor in explaining variance dependent variable. rationale is pred...