The core cover in relation to the nucleolus and the Weber set

Abstract

Core cover, core, Weber set, nucleolus, bankruptcy games, clan games, C71,

Characterizing the Core Via K-Core Covers

“…Then, Quant et al (2005) introduce and characterize the class of compromise stable games, which are those games that are compromise admissible and for which the core and the core cover coincide. Here, we perform a similar analysis for so called k-compromise stable games.…”

A note on the nucleolus for 2-convex TU games

“…Remark 2.4 In Quant et al (2005), the authors study the so-called class of compromise stable games of which the core agrees with a certain core cover in the sense of (1.6) by replacing the weak lower bound v({i}) by another sharp lower bound amounting b v i − min S i g v (S). Their approach to determine the nucleolus of compromise stable games games is totally different and strongly based on the study of (convex) bankruptcy games (Quant et al 2005, Theorem 4.2, pp.…”

Nontransferable Utility Bankruptcy Games

“…Moreover, Curiel et al (1987) show that the compromise value of bankruptcy games can be interpreted as an adjusted proportional rule for the underlying bankruptcy problem. Quant et al (2005) show that the class of bankruptcy games is the only class of games that satisfies both convexity and compromise stability, up to S-equivalence. For a survey on TU-bankruptcy, we refer to Thomson (2003).…”

“…O'Neill (1982) defines associated bankruptcy games and shows that these are convex games; Aumann and Maschler (1985) propose the Talmud rule as a solution to bankruptcy problems and show that this rule corresponds to the nucleolus of the associated bankruptcy game; Curiel, Maschler Tijs (1987) show that the (nonempty) core and the core cover of bankruptcy games coincide. In the (later) terminology of Quant, Borm, Reijnierse and van Velzen (2005), this means that bankruptcy games are compromise stable. Moreover, Curiel et al (1987) show that the compromise value of bankruptcy games can be interpreted as an adjusted proportional rule for the underlying bankruptcy problem.…”

“…In line with Estévez-Fernández, Fiestras-Janeiro, Mosquera and Sánchez (2012), we show that the core cover of a compromise admissible NTU-game can be obtained as the translation of the core cover of an associated NTU-bankruptcy game. Following Quant et al (2005), we define compromise stable NTU-games as those NTU-games with nonempty core for which the core and the core cover coincide.…”