The generalized Nash game proposed by Rosen

John Edwin Cotrina Asto; Carlos Calderon

doi:10.48550/arXiv.2307.03532

The generalized Nash game proposed by Rosen

John Edwin Cotrina Asto
, Carlos Calderon

Research output: Working paper

Abstract

We deal with the generalized Nash game proposed by Rosen, which is a game
with strategy sets that are coupled across players through a shared constraint. A
reduction to a classical game is shown, and as a consequence, Rosen’s result can be deduced from the one given by Arrow and Debreu. We also establish necessary and sufficient conditions for a point to be a generalized Nash equilibrium employing the variational inequality approach. Finally, some existence results are given in the non-compact case under coerciveness conditions.

Original language	English
Publisher	Cornell University
Pages	1-20
DOIs	https://doi.org/10.48550/arXiv.2307.03532
State	Published - 10 Jul 2023

Bibliographical note

arXiv:2307.03532v1 ([Submitted on 7 Jul 2023]

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title = "The generalized Nash game proposed by Rosen",

abstract = "We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen{\textquoteright}s result can be deduced from the one given by Arrow and Debreu. We also establish necessary and sufficient conditions for a point to be a generalized Nash equilibrium employing the variational inequality approach. Finally, some existence results are given in the non-compact case under coerciveness conditions.",

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AB - We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen’s result can be deduced from the one given by Arrow and Debreu. We also establish necessary and sufficient conditions for a point to be a generalized Nash equilibrium employing the variational inequality approach. Finally, some existence results are given in the non-compact case under coerciveness conditions.

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The generalized Nash game proposed by Rosen

Abstract

Bibliographical note

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