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Theory for Equilibria

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Nonlinear Programming Techniques for Equilibria

Part of the book series: EURO Advanced Tutorials on Operational Research ((EUROATOR))

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Abstract

Basic theoretical topics such as the existence of solutions, their stability and error bounds are analysed for the Ky Fan inequality

$$\displaystyle \begin{aligned} \text{find } \bar{x}\in C \text{ such that } f(\bar{x},y) \geq 0 \text{ for all } y\in C,\end{aligned} $$
(EP(f,C))

where \(C\subseteq \mathbb {R}^n\) is nonempty, convex and closed while \(f:\mathbb {R}^n\times \mathbb {R}^n\rightarrow \mathbb {R}\) is an equilibrium bifunction, i.e., it satisfies f(x, x) = 0 for any \(x\in \mathbb {R}^n\).

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Authors and Affiliations

  1. Department of Computer Science, University of Pisa, Pisa, Italy

    Giancarlo Bigi, Massimo Pappalardo & Mauro Passacantando

  2. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Marco Castellani

Authors
  1. Giancarlo Bigi
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  2. Marco Castellani
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  3. Massimo Pappalardo
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  4. Mauro Passacantando
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Bigi, G., Castellani, M., Pappalardo, M., Passacantando, M. (2019). Theory for Equilibria. In: Nonlinear Programming Techniques for Equilibria. EURO Advanced Tutorials on Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-030-00205-3_2

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