Pith. Sign in

RECORD

The Stackelberg Game: responses to regular strategies

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Thomas Byrne

Computational Geometry · Submitted 11 Nov 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 0.91 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2211.06472 (version 1)
Pith IDNRHPADYM, Pith's permanent record of this paper and its review
CitationThomas Byrne. "The Stackelberg Game: responses to regular strategies." arXiv:2211.06472 (2022). https://pith.science/paper/NRHPADYM
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,886 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.50 · human participants 0.03 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.74 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.10 0.03 hedged possibility 1.00
s1 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. contribution 0.58 0.12 0.10 asserted 0.93
s2 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. gap 0.65 0.52 0.24 asserted 0.91
s3 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. method 0.74 0.28 0.08 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from literature 0.48.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.