Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi payoff

A new concept for TU-values, called value dividends, is introduced. Similar to Harsanyi dividends, value dividends are defined recursively and provide new characterizations of values from the Harsanyi set. In addition, we generalize the Harsanyi set where each of the TU-values from this set is defined by the distribution of the Harsanyi dividends via sharing function systems and give an axiomatic characterization. As a TU value from the generalized Harsanyi set, we present the proportional Harsanyi payoff, a new proportional solution concept. As a side benefit, a new characterization of the Shapley value is proposed. None of our characterizations uses additivity

Disjointly and jointly productive players and the Shapley value

Central to this study is the concept of disjointly productive players where no cooperation gain occurs when one of two such players joins a coalition containing the other. Our first new axiom states that the payoff to a player does not change when another player, disjointly productive to that player, leaves the game. The second axiom implies that the payoff to a third player does not change if we merge two disjointly productive players into a new player. These two axioms, along with efficiency, characterize the Shapley value and may be advantageous sometimes to improve the runtime for computing the Shapley value. Further axiomatizations are provided, using, for example, a modification of behavior property where the payoff for two players in two new games in which their behavior changes once to total dislike and once to total affection is equal to the payoff in the original game