The selectope for cooperative games
The authors investigate the distribution of payoff within a coalition. As usual, a cooperative game is defined by the value function on coalitions. A set of distributions is constructed in the following way. The difference of the value of a coalition and the summarized value of all its sub-coalitions forms the dividend of Harsanyi. A selector is a function that assigns some element for every coalition. At last, the selector value of a player is the total value of dividends of all coalitions for which it is a selector. \textit{P. L. Hammer, U. N. Peled} and \textit{S. Sorensen} [Cah. Cent. Étud. Rech. Opér. 19, 159-176 (1977; Zbl 0362.90143)] introduced the notion of selectop, that is a convex hull of selector values on the set of all selectors. Analogs of the selector value and selectop are the well-known marginal value and Weber set. The authors construct the selector that generates the marginal value, so the Weber set is a subset of the selectop. Factors under which the selectop and Weber set coincide are found. Besides, a selectop contains weighted Shapley values and random order values. The authors find a simple way to prove the result of P. L. Hammer et al. that the selectop includes a core of the game. Several examples illustrate assertions and results.
scientific article; zbMATH DE number 1435956