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      Pedestrian motion modelled by Fokker–Planck Nash games

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          Abstract

          A new approach to modelling pedestrians' avoidance dynamics based on a Fokker–Planck (FP) Nash game framework is presented. In this framework, two interacting pedestrians are considered, whose motion variability is modelled through the corresponding probability density functions (PDFs) governed by FP equations. Based on these equations, a Nash differential game is formulated where the game strategies represent controls aiming at avoidance by minimizing appropriate collision cost functionals. The existence of Nash equilibria solutions is proved and characterized as a solution to an optimal control problem that is solved numerically. Results of numerical experiments are presented that successfully compare the computed Nash equilibria to the output of real experiments (conducted with humans) for four test cases.

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          Most cited references 36

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          Pedestrian route-choice and activity scheduling theory and models

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            A mathematical model for the behavior of pedestrians

             Dirk Helbing (1991)
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              On a mean field game approach modeling congestion and aversion in pedestrian crowds

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                Author and article information

                Journal
                R Soc Open Sci
                R Soc Open Sci
                RSOS
                royopensci
                Royal Society Open Science
                The Royal Society Publishing
                2054-5703
                September 2017
                13 September 2017
                13 September 2017
                : 4
                : 9
                Affiliations
                [1 ]Institut für Mathematik, Universität Würzburg , Emil-Fischer-Strasse 30, 97074 Würzburg, Germany
                [2 ]Université Côte d'Azur , Inria, CNRS, LJAD, UMR 7351, Parc Valrose, 06108 Nice, France
                Author notes

                Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3874486.

                Article
                rsos170648
                10.1098/rsos.170648
                5627107
                © 2017 The Authors.

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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                Categories
                1008
                6
                1001
                42
                119
                Mathematics
                Research Article
                Custom metadata
                September, 2017

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