Rosenthal’s potential and a discrete version of the Debreu–Gorman Theorem

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthal-style construction if aggregation rules of all players are “quasi-separable.” Each universal separable ordering on a finite set can be represented as a combination of addition and lexicography.