Abstract
The aim of the paper is to study an evolutionary quasi-variational inequality, which expresses the equilibrium conditions of a general oligopolistic market equilibrium model, and to present its inverse formulation.
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Notes
We recall that in the Hilbert space \(L^2([0,T], \mathbb {R}^k)\) we define the canonical bilinear form on \(L^2([0,T], \mathbb {R}^k) \times L^2([0,T], \mathbb {R}^k)\) given by
$$\begin{aligned} \ll \phi , w \gg := \in _0^T \langle \phi (t), w(t) \rangle dt, \end{aligned}$$where \(\phi \in L^2([0,T], \mathbb {R}^k)\).
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Acknowledgments
The first author was partially supported by STAR 2014 “Variational Analysis and Equilibrium Models in Physical and Socio-Economic Phenomena” (Grant 14-CSP3-C03-099). The authors would like to thank the referees for the helpful comments and suggestions which led to a clearer presentation of this work.
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Communicated by Jean-Pierre Crouzeix.
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Barbagallo, A., Mauro, P. A General Quasi-variational Problem of Cournot-Nash Type and Its Inverse Formulation. J Optim Theory Appl 170, 476–492 (2016). https://doi.org/10.1007/s10957-016-0924-z
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DOI: https://doi.org/10.1007/s10957-016-0924-z