Construction of Compromise Values for Cooperative Games

Abstract

We explore a broad class of values for cooperative games in characteristic function form, known as compromise values. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs. We identify subclasses of games that admit non-trivial efficient allocations within the considered bounds, which we call \emph{bound-balanced games}. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using variants of the minimal rights property and restricted proportionality. We introduce two construction methods for properly devised compromise values. Under mild conditions, one can use either a lower or an upper bound to construct a well-defined compromise value. Based on these methods, we construct and axiomatise various well-known and new compromise values, including the $τ$-, the $χ$-, the Egalitarian, the Gately, the CIS-, the PANSC-, the EANSC-, and the new KM-values. We conclude that this approach establishes a common foundation for a wide range of different values.