Supplement to Game Theory and Ethics

Long descriptions for some figures in Game Theory and Ethics

Figure 2 description

A decision tree

  • Laura (root node)
    • \((2,2)\) (node; line to it labeled P)
    • \((0,3)\) (node; line to it labeled A)

Figure 3 description

A decision tree

  • Claudia (root node)
    • Laura (node; line to it labeled P)
      • \((2,2)\) (node; line to it labeled P)
      • \((0,3)\) (node; line to it labeled A)
    • Laura (node; line to it labeled A)
      • \((3,0)\) (node; line to it labeled P)
      • \((1,1)\) (node; line to it labeled A)

Figure 4 description

A decision tree

  • Claudia (root node)
    • Laura (node; line to it labeled P)
      • \((2,2)\) (node; line to it labeled P)
      • \((0,{3-\gamma})\) (node; line to it labeled A)
    • Laura (node; line to it labeled A)
      • \((3,0)\) (node; line to it labeled P)
      • \((1,1)\) (node; line to it labeled A)

Figure 9 description

A x-y graph with a labeled center of \((0,0)\). on it is a green shaded triangle region with vertices at \((0,1),\) \((1,0),\) and \((-1,-1)\) [also labeled ‘Nonagreement Point’]. The labeled point \((\frac{1}{2},\frac{1}{2})\) is on the line between the first and second points.

Figure 11 description

A x-y graph with x and y axes ranging from 0 to 1. On it is a green shaded quadrilateral region with vertices \((0, \frac{1}{9})\), \((\frac{1}{2},1)\), \((1, \frac{2}{9})\), and \((\frac{1}{6},;0)\). On the line connecting the second and third points are three more points each also labeled:

  • \((0.536,0.944)\) Nash
  • \((0.652,0.763)\) proportional
  • \((0.682,0.717)\) maximin proportionate gain

Figure 12 description

An equilateral triangle with vertices labeled counterclockwise:

  • \(e_1(D)\)
  • \(e_2(M)\)
  • \(e_3(H)\)

A path is drawn connecting a sequence of points starting from a point towards the middle of the triangle, heading down and curving towards the towards the second vertex \(e_2(M)\).

Figure 13 description

Same equilateral triangle as Figure 12 with vertices labeled counterclockwise:

  • \(e_1(D)\)
  • \(e_2(M)\)
  • \(e_3(H)\)

The interior of the triangle has 200 curves starting at various points around the interior of the triangle. Most of these individual curves bend towards a single central curve that runs from about half way between the first and third vertices and ultimately ends converges to the second vertex. But a few of these curves, with starting points especially close to the first or third vertex bend toward that same central curve but converge to a point about half way between the first and third vertex.

Figure 14 description

Same equilateral triangle as Figure 12 with vertices labeled counterclockwise:

  • \(e_1(D)\)
  • \(e_2(M)\)
  • \(e_3(H)\)

The interior of the triangle has 200 curves starting at various points around the interior of the triangle. All of the individual curves bend towards a single central curve that runs from about half way between the first and third vertices and ultimately converges to the second vertex.

Figure 15 descriptions

Each of the figures 15a through 15d is a grid of squares \(20\times 20\) with each square either blue (one agent), red (the other agent), or white (empty). Figure 15a has the colors the most mingled; figure 15b has some clumping of colors, figure 15c some more clumping of colors (4 red regions, 5 blue regions), and figure 15d the most (2 red regions, 3 blue regions).

Copyright © 2021 by
Keith Hankins <keith.s.hankins@gmail.com>
Peter Vanderschraaf <pvanderschraaf@arizona.edu>

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