The Stackelberg Game: responses to regular strategies

TL;DR

This paper explores the Stackelberg variant of the Voronoi game, analyzing how the first player can mitigate second player's advantages in territory division through strategic placements.

Contribution

It extends the analysis of Voronoi games to the Stackelberg setting, focusing on strategies for White to minimize Black's territorial gains.

Findings

White's grid arrangements can be exploited by Black

Strategies for White to mitigate damage are identified

Transfer of results from One-Round Voronoi Game to Stackelberg game

Abstract

Following the solution to the One-Round Voronoi Game in arXiv:2011.13275, we naturally may want to consider similar games based upon the competitive locating of points and subsequent dividing of territories. In order to appease the tears of White (the first player) after they have potentially been tricked into going first in a game of point-placement, an alternative game (or rather, an extension of the Voronoi game) is the Stackelberg game where all is not lost if Black (the second player) gains over half of the contested area. It turns out that plenty of results can be transferred from One-Round Voronoi Game and what remains to be explored for the Stackelberg game is how best White can mitigate the damage of Black's placements. Since significant weaknesses in certain arrangements were outlined in arXiv:2011.13275, we shall first consider arrangements that still satisfy these results (namely, White plays a certain grid arrangement) and then explore how Black can best exploit these positions.