Last minute panic in zero sum games^*

¹ Institute for Mathematics, University of Jena, Ernst-Abbe-Platz 2, 07745 Jena, Germany.
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: christophette.blanchet@ec-lyon.fr

Received: 18 January 2017
Accepted: 14 February 2018

Abstract

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.