The Barrier Surface in the Cooperative Football Differential Game

TL;DR

This paper analyzes a pursuit-evasion game in football, deriving the barrier surface that separates winning strategies for pursuers and evaders, and provides a method to determine the winning team under optimal play.

Contribution

It introduces the explicit construction of the barrier surface for the football pursuit-evasion game, enabling the determination of winning regions under optimal strategies.

Findings

Barrier surface partitions state space into winning sets.

Optimal play determines the winning team via the Barrier function.

Provides a solution to the game of kind for this pursuit-evasion scenario.

Abstract

This paper considers the blocking or football pursuit-evasion differential game. Two pursuers cooperate and try to capture the ball carrying evader as far as possible from the goal line. The evader wishes to be as close as possible to the goal line at the time of capture and, if possible, reach the line. In this paper the solution of the game of kind is provided: The Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is constructed. Under optimal play, the winning team is determined by evaluating the associated Barrier function.