We provide a new interpretation of the potential of the Shapley value as the expected worth of some random partition of the player set. Using this insight, we advocate the potential as an index of power concentration in simple monotonic games.

The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player's marginal contribution to all coalitions increase or stay the same, then this player's payoff should not decrease. We investigate the class of values...

Within a simple setup, we show that proportional taxation is implied by three properties: efficiency, symmetry, and monotonicity. Efficiency: redistribution has no cost. Symmetry: members of the society with the same performance obtain the same reward after redistribution. Monotonicity: whenever...

The Coleman Power of the Collectivity to Act (CPCA) is a popular statistic that reflects the ability of a committee to pass a proposal. Applying the Shapley value to this measure, we derive a new power index that indicates each voter's contribution to the CPCA. This index is characterized by...

We introduce the concepts of the components' second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components' second-order payoffs for one-point solutions for CS games as generalizations of the players'...

We provide new characterisations of the equal surplus division value. This way, the difference between the Shapley value, the equal surplus division value, and the equal division value is pinpointed to one axiom.

We suggest a new one-parameter family of solidarity values for TU-games. The members of this class are distinguished by the type of player whose removal from a game does not affect the remaining players’ payoffs. While the Shapley value and the equal division value are the boundary members of...