Weak differential marginality and the Shapley value

Steady Marginality: A Uniform Approach to Shapley Value for Games with Externalities

The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in many realistic applications where externalities are present, Shapley’s axioms fail to indicate such a unique division. Consequently, there are many extensio...

The Marginality Approach for the Shapley Value in Games with Externalities

One of the long-debated issues in coalitional game theory is how to extend the Shapley to games with externalities (partition-function games). When externalities are present, not only can a player’s marginal contribution to a coalition—a central notion to the Shapley value—be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of ...

Marginality Approach To Shapley Value In Games With Externalities

The Shapley value without efficiency and additivity

We provide a new characterization of the Shapley value neither using the e¢ciency axiom nor the additivity axiom. In this characterization, e¢ciency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615–621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are ...

Alternative Axiomatic Characterizations of the Grey Shapley Value

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapl...