Supplement to Epistemic Foundations of Game Theory

Long descriptions for some figures in Epistemic Foundations of Game Theory

Figure 2 description

A tree diagram of three levels. A root node, labeled \(d_0\) at the top with lines going from it to two nodes below, with the left node labeled \(d_1\) and the right node \(d_2\). From each of those nodes two more lines go to nodes at the bottom, under \(d_1\) the nodes are labeled \(o_1\) and \(o_2\) and under \(d_2\) the nodes are labeled \(o_1\) and \(o_2\). A dashed rectangle encloses \(d_1\) and \(d_2\) nodes (the second level).

Figure 3 description

a diagram with the word “start” at the top and line going down from it with three equidistant circle nodes on it labeled X, Y, and C. At node X a line labeled “EXIT” goes to the right to a circle node labeled A and the number 0. At node Y a line labeled “EXIT” goes to the right to a circle node labeled B and the number 4. Both the line between nodes X and Y and the line between nodes Y and C are labeled “Cont”. Beside node C is the number 1. A dashed line rectangle encloses nodes X and Y and the line between them.

Figure 5 description

A diagram of four circle nodes in a square. The two top nodes are connected by a solid line labeled a and the same with the two bottom nodes; the two right nodes are connected by a dashed line labeled b and the same with the two left nodes.

The four nodes are

  • top left circle node encloses the text \(u,l\) and is labeled \(w_1\).
  • bottom left circle node encloses the text \(d,l\) and is labeled \(w_2\).
  • top right circle node encloses the text \(u,r\) and is labeled \(w_3\).
  • bottom right circle node encloses the text \(d,r\) and is labeled \(w_4\).

Enclosing the two top circle nodes (\(w_1\) and \(w_3\)) is a gray jagged rectangle labeled U.

Figure 6 description

Very similar to figure 5 so we'll repeat the description then note the differences from figure 5

A diagram of four circle nodes in a square. The two top nodes are connected by a solid line labeled a and the same with the two bottom nodes; the two right nodes are connected by a dashed line labeled b and the same with the two left nodes.

The four nodes are

  • top left circle node encloses the text \(u,l\) and is labeled \(w_1\).
  • bottom left circle node encloses the text \(d,l\) and is labeled \(w_2\).
  • top right circle node encloses the text \(u,r\) and is labeled \(w_3\).
  • bottom right circle node encloses the text \(d,r\) and is labeled \(w_4\).

The differences from figure 5 are that there is a circle node to the left of the top left node \(w_1\) which is labeled \(w'\) and encloses the text \(u,l\); the solid line connecting it to node \(w_1\) which is labeled a; and the gray jagged rectangle labeled U which encloses all three top circle nodes (\(w'\), \(w_1\), \(w_3\)).

Figure 7 description

A diagram of 6 circle nodes in a grid two high and three wide and labeled left to right on the top \(w_1\) to \(w_3\) and on the bottom \(w_4\) to \(w_6\). Each vertical pair is enclosed by a dashed line rectangle and each horizontal triplet by a solid line rectangle.

  • \(w_1\) node (top right) encloses the text \(u,l\) and has the fraction “1/8” by it
  • \(w_2\) node encloses the text \(u,r\) and has the fraction “1/8” by it
  • \(w_3\) node encloses the text \(u,r\) and has the number “0” by it
  • \(w_4\) node (bottom right) encloses the text \(d,l\) and has the fraction “1/8” by it
  • \(w_5\) node encloses the text \(d,r\) and has the fraction “1/8” by it
  • \(w_6\) node encloses the text \(d,r\) and has the fraction “1/2” by it

A shaded gray region includes nodes \(w_2\), \(w_5\), and \(w_6\).

Figure 11 description

A diagram of 8 solid circle nodes in a grid two high and four wide. Each vertical pair is enclosed by a dashed line rectangle and each horizontal set of four is enclosed by a solid line rectangle.

For each node top to bottom left to right:

  • top first node has \((t_1,t'_1,u,l)\) above it and \(p_a=0.25\) and \( p_b=0.25\) below it
  • top second node has \((t_1,t'_2,u,l)\) above it and \(p_a=0.20\) and \( p_b=0.05\) below it
  • top third node has \((t_1,t'_1,u,r)\) above it and \(p_a=0.00\) and \(p_b=0.25\) below it
  • top fourth node has \((t_1,t'_2,u,r)\) above it and \(p_a=0.05\) and \(p_b=0.05\) below it
  • bottom first node has \((t_1,t'_1,d,l)\) above it and \(p_a=0.25\) and \(p_b=0.00\) below it
  • bottom second node has \((t_1,t'_2,d,l)\) above it and \(p_a=0.20\) and \(p_b=0.20\) below it
  • bottom third node has \((t_1,t'_1,d,r)\) above it and \(p_a=0.0\) and \(p_b=0.0\) below it
  • bottom fourth node has \((t_1,t'_2,d,r)\) above it and \(p_a=0.05\) and \(p_b=0.20\) below it

Figure 17 description

A diagram of 3 horizontal circle nodes labeled \(v_1\), \(v_2\), \(v_3\). Below each circle node is a rounded rectangle nodes labeled respectively \(o_1\), \(o_2\), and \(o_3\). A fourth rounded rectangle node labeled \(o_4\) is to the right of \(v_3\).

\(v_1\) connects to \(v_2\) with a solid line labeled \(I_1\); \(v_2\) connects to \(v_3\) with a solid line labeled \(I_2\); and \(v_3\) to \(o_4\) with a solid line labeled \(I_3\). Solid lines also connect each circle node to the rounded rectangle below and are labeled respectively \(O_1\), \(O_2\), \(O_3\). The nodes enclose:

  • Circle nodes \(v_1\) and \(v_3\) enclose the text A
  • Circle node \(v_2\) encloses the text B
  • Rectangle node \(o_1\) encloses \(1,1\)
  • Rectangle node \(o_2\) encloses \(0,2\)
  • Rectangle node \(o_3\) encloses \(4,1\)
  • Rectangle node \(o_4\) encloses \(3,3\)

Figure 18 description

Very similar to figure 17 so we will repeat most of Figure 17’s description and describe the changes from Figure 17 after.

A diagram 3 horizontal circle nodes labeled \(v_1\), \(v_2\), \(v_3\). Below each circle node is a rounded rectangle nodes labeled respectively \(o_1\), \(o_2\), and \(o_3\). A fourth rounded rectangle node labeled \(o_4\) is to the right of \(v_3\).

\(v_1\) connects to \(v_2\) with a solid line labeled \(I_1\); \(v_2\) connects to \(v_3\) with a solid line labeled \(I_2\); and \(v_3\) to \(o_4\) with a solid line labeled \(I_3\). Solid lines also connect each circle node to the rounded rectangle below and are labeled respectively \(O_1\), \(O_2\), \(O_3\).

The changes from Figure 17 are in what nodes \(o_1\) through \(o_3\) enclose:

  • Circle nodes \(v_1\) and \(v_3\) enclose the text A
  • Circle node \(v_2\) encloses the text B
  • Rectangle node \(o_1\) encloses \(2,2\)
  • Rectangle node \(o_2\) encloses \(1,1\)
  • Rectangle node \(o_3\) encloses \(0,0\)
  • Rectangle node \(o_4\) encloses \(3,3\)

Figure 23 description

A diagram including a decision table. Circle node A has a vertical line labeled O to a rectangle enclosing \(2,2\). It also has a horizontal line labeled I to the

    B
    l r
A u \(3,1\) \(0,0\)
d \(0,0\) \(1,3\)

Copyright © 2025 by
Eric Pacuit <epacuit@umd.edu>
Olivier Roy <Olivier.Roy@uni-bayreuth.de>

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