An average lexicographic value for cooperative games

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.

► The Alexia value is a new allocation rule for cooperative games.
► The Alexia value combines attractive properties of the Shapley value and the nucleolus.
► For convex games the Alexia value and the Shapley value coincide.
► For subclasses of compromise stable games an expression for the Alexia value is derived.