A note on the permutationally convex games
An \(n\)-person side-payment game \(v\) is called permutationally convex with an ordering \(\pi\) on the player set, if \[ v(P^ \pi_ j\cup\{j\}\cup S)-v(P^ \pi_ j\cup\{j\})\leq v(P^ \pi_ k\cup\{k\}\cup S)-v(P^ \pi_ k\cup\{k\}) \] for all \(k\geq j\) and \(S\subset N\backslash[P^ \pi_ k\cup\{k\}]\), where \(P^ \pi_ j:=\{i\mid\pi(i)<\pi(j)\}\). It is well-known that a permutationally convex game with an ordering \(\pi\) has its marginal worth vector with respect to \(\pi\) as a member of the core. This paper shows by an example that the converse is false.
scientific article; zbMATH DE number 9436