This paper characterizes the aspects of exchangeability in the Shapley value. We show that, in the Shapley value, each player’s prospects of joining a t-player game as the last member of the game is a moment sequence of the uniform distribution. We prove that, with finite exchangeability, the Shapley value is the only value in which the probability assignment is a unique mixture of independent ...

Suppose that G is a Lie group. which for the purpose of this introduction, we take to be a real form of a simply connected complex semisimple group. Suppose that square integrable representations for G exist and that f is a matrix coefficient of a square integrable representation belonging to the unitary equivalence class co. Harish-Chandra has shown how to evaluate the integral off with respec...

The prints of the Palomar Sky Survey, luminosity classification and radial velocities were used to assign all northern Shapley-Ames galaxies to either (1) field, (2) group, or (3) cluster environments. This information for 930 galaxies shows no evidence for a dependence of bar frequency on galaxy environment. This suggests that the formation of a bar in a disk galaxy is mainly determined by the...

We introduce a new stability concept for multi-period matching markets. Robust prescient stability asserts that agents exhibit foresight concerning how a market can develop in the future, but they retain ambiguity concerning how the market will develop. We show that a robustly presciently stable matching exists for any configuration of agents’ preferences.

We show that any transferable utility game can be represented by an assignment of facilities to the players, in which it is intuitively obvious how to allocate the total cost of the facilities. The intuitive solution in the representation turns out to be the Shapley value of the game, and thus serves as an alternative justification of the value.

Divergent selection and adaptive divergence can increase phenotypic diversification amongst populations and lineages. Yet adaptive divergence between different environments, habitats or niches does not occur in all lineages. For example, the colonization of freshwater environments by ancestral marine species has triggered adaptive radiation and phenotypic diversification in some taxa but not in...