Construction of compromise values for cooperative games - Robert Paul Gilles; René van den Brink (Tinbergen Institute, 2025)
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 wellspecified upper and lower bounds on payoffs. We identify subclasses of games that admit nontrivial efficient allocations within the considered bounds, which we call bound-balanced games. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using a combination of the minimal-rights property and a variant of restricted proportionality. We construct and axiomatise various well-known and new compromise values based on these methods, including the 𝜏-, the 𝜒-, 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.
Keywords: C71; 330; Cooperative TU-game; compromise value; 𝜏 -value; CIS value; Gately value; KM-value; axiomatisation; bound balanced games