New and recent axioms for cooperative games with transferable utilities are introduced. The non-negative player axiom requires to assign a non-negative payoff to a player that belongs to coalitions with non-negative worth only. The axiom of addition invariance on bi-partitions requires that the payoff vector recommended by a value should not be affected by an identical change in worth of both a coalition and the complementary coalition. The nullified solidarity axiom requires that if a player who becomes null weakly loses (...) from such a change, then every other player should weakly lose too. We study the consequence of imposing some of these axioms in addition to some classical axioms. It turns out that the resulting values or set of values have all in common to split efficiently the worth achieved by the grand coalition according to an exogenously given weight vector. As a result, we also obtain new characterizations of the equal division value. (shrink)

We revisit the characterization of the Shapley value by van den Brink (Int J Game Theory, 2001, 30:309–319) via efficiency, the Null player axiom, and some fairness axiom. In particular, we show that this characterization also works within certain classes of TU games, including the classes of superadditive and of convex games. Further, we advocate some differential version of the marginality axiom (Young, Int J Game Theory, 1985, 14: 65–72), which turns out to be equivalent to the van den Brink (...) fairness axiom on large classes of games. (shrink)

We provide another characterization of the Owen value for TU games with a coalition structure without the additivity axiom.

We revisit the Nowak (Int J Game Theory 26:137–141, 1997) characterization of the Banzhaf value via 2-efficiency, the Dummy player axiom, symmetry, and marginality. In particular, we provide a brief proof that also works within the classes of superadditive games and of simple games. Within the intersection of these classes, one even can drop marginality. Further, we show that marginality and symmetry can be replaced by van den Brink fairness/differential marginality. For this axiomatization, 2-efficiency can be relaxed into superadditivity on (...) the full domain of games. (shrink)

We present experimental data on a simple market game. Several solution concepts from cooperative game theory are applied to predict the observed payoff distributions. Notably, a recently introduced solution concept meant to capture the influence of outside options on the payoff distribution within groups fares better than most other solution concepts under consideration. Our results shed some light on the effects of scarcity relations on markets on bargaining outcomes within negotiating dyads.