@inbook{e5bef219e78642c9b87387011b787c17,
title = "The Outcomes of Generative AI Are Exactly the Nash Equilibria of a Non-potential Game",
abstract = "In this article we show that the asymptotic outcomes of both shallow and deep neural networks such as those used in BloombergGPT to generate economic time series are exactly the Nash equilibria of a non-potential game. We then design and analyze deep neural network algorithms that converge to these equilibria. The methodology is extended to federated deep neural networks between clusters of regional servers and on-device clients. Finally, the variational inequalities behind large language models including encoder-decoder related transformers are established.",
keywords = "Activation function, Deep learning, Nash equilibrium, Neural network, potential game, Stackelberg game, γ-averaging",
author = "Boualem Djehiche and Tembine Hamidou",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",
year = "2024",
doi = "10.1007/978-3-031-59110-5_4",
language = "English (US)",
series = "Studies in Systems, Decision and Control",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "57--80",
booktitle = "Studies in Systems, Decision and Control",
address = "Germany",
}