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Abstracting Nash equilibria of supermodular games

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Abstract

Supermodular games are a well known class of noncooperative games which find significant applications in a variety of models, especially in operations research and economic applications. Supermodular games always have Nash equilibria which are characterized as fixed points of multivalued functions on complete lattices. Abstract interpretation is here applied to set up an approximation framework for Nash equilibria of supermodular games. This is achieved by extending the theory of abstract interpretation in order to cope with approximations of multivalued functions and by providing some methods for abstracting supermodular games, thus obtaining approximate Nash equilibria which are shown to be correct within the abstract interpretation framework.

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Acknowledgements

The author thanks the anonymous reviewers for their useful suggestions. The author has been partially supported by the University of Padova under the PRAT project “ANCORE” no. CPDA148418.

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  1. Dipartimento di Matematica, University of Padova, Padova, Italy

    Francesco Ranzato

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  1. Francesco Ranzato
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Correspondence to Francesco Ranzato.

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Ranzato, F. Abstracting Nash equilibria of supermodular games. Form Methods Syst Des 53, 259–285 (2018). https://doi.org/10.1007/s10703-017-0291-x

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