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Distributed Nash equilibrium tracking via the alternating direction method of multipliers

Ji MaZheng YangZiqin Chen — 2023

Kybernetika

Nash equilibrium is recognized as an important solution concept in non-cooperative game theory due to its broad applicability to economics, social sciences, computer science, and engineering. In view of its importance, substantial progress has been made to seek a static Nash equilibrium using distributed methods. However, these approaches are inapplicable in dynamic environments because, in this setting, the Nash equilibrium constantly changes over time. In this paper, we propose a dynamic algorithm...

Associated graded rings and connected sums

H. AnanthnarayanEla CelikbasJai LaxmiZheng Yang — 2020

Czechoslovak Mathematical Journal

In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q , which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré...

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