Volume 25, 2019
|Number of page(s)||17|
|Published online||30 July 2019|
Last minute panic in zero sum games*
Institute for Mathematics, University of Jena,
2 Université de Lyon – CNRS, UMR 5208, Institut Camille Jordan – Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France.
3 Institute for Mathematics, University of Jena, Ernst-Abbe-Platz 2, 07745 Jena, Germany.
** Corresponding author: firstname.lastname@example.org
Accepted: 14 February 2018
We set up a game theoretical model to analyze the optimal attacking intensity of sports teams during a game. We suppose that two teams can dynamically choose among more or less offensive actions and that the scoring probability of each team depends on both teams’ actions. We assume a zero sum setting and characterize a Nash equilibrium in terms of the unique solution of an Isaacs equation. We present results from numerical experiments showing that a change in the score has a strong impact on strategies, but not necessarily on scoring intensities. We give examples where strategies strongly depend on the score, the scoring intensities not at all.
Mathematics Subject Classification: 49K35 / 49M25 / 91A05
Key words: Nash equilibrium / Isaacs equation / Zero-sum games
© EDP Sciences, SMAI 2019
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