Self-covariant and consistent solutions of transferable utility cooperative games

Automation and Remote Control. 2018. Vol. 79. No. 12. P. 2237–2258.

E.B.Yanovskaya

A weakening of the property covariance named self-covariance is defined. Sels-covariant solutions are positively homogenous and satisfy a "restricted" translation covariance  so that feasible shifts are only the solution vectors and their multipliers. A description of all non-empty, single-valued,efficient,anonytmous, weakly and self-covariant solutions inn the class of two-person games is given. As demonstrated below, among them there exist just three solutions admitting consistent extensions in the Davis--Maschler sense. They are the equal share solution, the stansdard solution, and the constrained ergalitarian solution for super-additive two-person games. For the third solution mentioned, characterizations of some consistent extensions to the class of all TU games are given.

Keywords: кооперативная игра, covariance, ковариантность, cooperative game, self-covariance, consistent extensions, само-ковариантность, equal share solution, standard solution, constrained egalitarian solution, стандартное решение, решение равных дележей, ограниченно эгалитарное решение, согласованное расширение

Publication based on the results of: Mechanism Design: modern approaches (2018)