Self-covariant and consistent solutions of cooperative games

A weakening of covariance property for solutions of cooperative games with transferable utilities – self-covariance – is defined. Self-covariant solutions are positively homogenous and satisfy a "restricted" translation covariance such that feasible shifts are only the solution vectors themselves and their multipliers. A description of all nonempty, efficient, anonymous, self-covariant, and single-valued solution for the class of two-person TU games is given. Among them the solutions admitting consistent extensions in the Davis–Maschler sense are found. They are the equal share solution, the standard solution, and the constrained egalitarian solution for superadditive two-person games. Characterizations of consistent extensions of these solutions to the class of all TU games are given.