scholarly journals The symmetry axiom in Minkowski planes

2006 ◽  
Vol 76 (1) ◽  
pp. 1-16
Author(s):  
J. Kosiorek ◽  
A. MatraŜ
Keyword(s):  
Minkowski Planes ◽  
Symmetry Axiom

Covering Discs in Minkowski Planes

2009 ◽  
Vol 52 (3) ◽  
pp. 424-434 ◽  
Author(s):  
Horst Martini ◽  
Margarita Spirova
Keyword(s):  
Essential Role ◽  
Covering Problem ◽  
Minkowski Geometry ◽  
Minkowski Planes ◽  
Strictly Convex ◽  
Unit Circles ◽  
Circle Covering ◽  
Monotonicity Lemma

AbstractWe investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by k unit circles. In particular, we study the cases k = 3, k = 4, and k = 7. For k = 3 and k = 4, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, d-segments, and the monotonicity lemma.

A Perspective-Invariant Approach to Nash Bargaining

2020 ◽  
Author(s):  
Barry Nalebuff
Keyword(s):  
Business Strategy ◽  
Ideal Point ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Disagreement Point ◽  
Equal Sacrifice ◽  
Symmetry Axiom ◽  
Bargaining Sets ◽  
Invariant Approach ◽  
Do So

The Nash axioms lead to different results depending on whether the negotiation is framed in terms of gains relative to no agreement or in terms of sacrifices relative to an ideal. We look for a solution that leads to the same result from both perspectives. To do so, we restrict the application of Nash’s IIA axiom to bargaining sets where all options are individually rational and none exceed either party’s ideal point. If we normalize the bargaining set so that the disagreement point is (0, 0) and maximal gains are (1, 1), then any perspective-invariant bargaining solution must lie between the Utilitarian solution and the maximal equal-gain (minimal equal-sacrifice) solution. We show that a modified version of Nash’s symmetry axiom leads to the Utilitarian solution and that a reciprocity axiom leads to the equal-gain (equal-sacrifice) solution, both of which are perspective invariant. This paper was accepted by Joshua Gans, Business Strategy.

Angle Measures and Bisectors in Minkowski Planes

2005 ◽  
Vol 48 (4) ◽  
pp. 523-534 ◽  
Author(s):  
Nico Düvelmeyer
Keyword(s):  
Unit Circle ◽  
Minkowski Plane ◽  
Arc Length ◽  
Area Measure ◽  
Angular Measure ◽  
Minkowski Planes ◽  
Length Measure

AbstractWe prove that a Minkowski plane is Euclidean if and only if Busemann's or Glogovskij's definitions of angular bisectors coincide with a bisector defined by an angular measure in the sense of Brass. In addition, bisectors defined by the area measure coincide with bisectors defined by the circumference (arc length) measure if and only if the unit circle is an equiframed curve.

4-dimensional Minkowski planes with large automorphism group

1992 ◽  
Vol 4 (4) ◽  
Author(s):  
Günter F. Steinke
Keyword(s):  
Automorphism Group ◽  
Minkowski Planes ◽  
Large Automorphism Group

scholarly journals On the symmetry axiom for values of nonatomic games

1990 ◽  
Vol 13 (1) ◽  
pp. 165-169 ◽  
Author(s):  
Dov Monderer ◽  
William H. Ruckle
Keyword(s):  
Nonatomic Games ◽  
Symmetry Axiom

In this paper, a weaker version of the Symmetry Axiom on BV, and values on subspaces of BV are discussed. Included are several theorems and examples.

A perimeter-based angle measure in Minkowski planes

2017 ◽  
Vol 92 (1) ◽  
pp. 135-163 ◽  
Author(s):  
Martin Obst
Keyword(s):  
Angle Measure ◽  
Minkowski Planes

Some Minkowski planes with 3-dimensional automorphism group

1985 ◽  
Vol 25 (1) ◽  
pp. 88-100 ◽  
Author(s):  
G�nter F. Steinke
Keyword(s):  
Automorphism Group ◽  
Minkowski Planes ◽  
3 Dimensional
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