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Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem

Kukushkin, Nikolai S. (2014): Rosenthal's potential and a discrete version of the Debreu--Gorman Theorem.

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Abstract

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." Every universal separable ordering on a finite set can be represented as a combination of addition and lexicography.

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