Rate of Loss Characterization that Resolves the Dilemma of the Wall Pursuit Game Solution

The scope of this work is the well-known wall pursuit game which has been used in the literature to illustrate the existence of a singular surface (dispersal line) and the associated game dilemma. We derive an analytical expression for the value function of the game and use a hold time to derive the rate of change for the loss of the time to capture along the dispersal line. Then we resolve the dilemma along the dispersal line using actions defined by the saddle point of the rate of change for the loss. Finally, we analyze the same game in a version with a non-zero hold time and show that in that case, the actions from the dispersal line have to be applied not only on the dispersal line, but in a narrow band around it. To illustrate that, we use an example to compute the band around the line.

DOI: 10.1109/TAC.2021.3137786