Automation and Remote Control

, Volume 79, Issue 12, pp 2237–2258

# Self-Covariant and Consistent Solutions of Transferable Utility Cooperative Games

• E. B. Yanovskaya
Mathematical Game Theory And Applications

## Abstract

This paper defines the self-covariance property for the solutions of transferable utility cooperative games (TU-games) as a weakening of their covariance. Self-covariant solutions are positively homogenous and satisfy a “restricted” translation covariance so that feasible shifts are only the solution vectors themselves and their multipliers. A description of all non-empty, single-valued, efficient, anonymous, weakly and self-covariant solutions in the class of twoplayer TU-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 standard solution, and the constrained egalitarian solution for superadditive two-player TUgames. For the third solution mentioned, characterizations of some consistent extensions to the class of all TU-games are given.

## Keywords

cooperative game covariance self-covariance equal share solution standard solution constrained egalitarian solution consistent extension

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