Generalised Gately Values of Cooperative Games

Game Theoretic Foundations of the Gately Power Measure for Directed Networks

“…These properties imply that ρ D is a regular TU-game as defined in Gilles and Mallozzi [31]. This implies that the Gately value applies to the TU-game ρ D .…”

“…Therefore, σ D is regular as defined in Gilles and Mallozzi [31]. Hence, the Gately value applies to σ D .…”

“…More recently, Staudacher and Anwander [30] generalised the scope of the Gately value and identified exact conditions under which this value is well-defined. This has further been developed by Gilles and Mallozzi [31], who showed that the Gately value is always a core imputation for three-player games, devised an axiomatisation for the Gately value for arbitrary TU-games and introduced a generalised Gately value founded on weighted propensities to disrupt.…”

“…The Gately value was seminally introduced by Gately [27] and further developed by Littlechild and Vaidya [28], Charnes et al [29], Staudacher and Anwander [30], and Gilles and Mallozzi [31].…”

“…Combined with the previous case, this shows the first assertion of the theorem. Finally, the second assertion of the theorem follows immediately from identifying the propensity to disrupt ( [31], Definition 3.2) in the successor representation ρ D for some game theoretic imputation m ∈ R N as…”