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1 | 1 | .. _dominated-strategies: |
2 | 2 |
|
3 | | -Investigating dominated strategies and actions |
4 | | -============================================== |
| 3 | +Investigating dominated strategies |
| 4 | +================================== |
5 | 5 |
|
6 | 6 | Selecting :menuselection:`Tools --> Dominance` |
7 | 7 | toggles the appearance of a toolbar which |
8 | | -can be used to investigate the structure of dominated strategies and |
9 | | -actions. |
10 | | - |
11 | | - |
12 | | - |
13 | | -Dominated actions in extensive game |
14 | | ------------------------------------ |
15 | | - |
16 | | -In extensive games, the dominance toolbar controls the elimination of actions which are conditionally dominated. |
17 | | - |
18 | | -.. image:: screens/pokerdom1.* |
19 | | - :width: 33% |
20 | | - :alt: the poker game, with the dominance toolbar shown |
21 | | - :align: right |
22 | | - :target: _images/pokerdom1.png |
23 | | - |
24 | | -Actions may be eliminated based on two criteria: |
25 | | - |
26 | | -:guilabel:`Strict dominance` |
27 | | - The action is always worse than another, |
28 | | - regardless of beliefs at the information set; |
29 | | - |
30 | | -:guilabel:`Strict or weak dominance` |
31 | | - There is another action at the information |
32 | | - set that is always at least as good as the action, and strictly better |
33 | | - in some cases. |
34 | | - |
35 | | -.. image:: screens/pokerdom2.* |
36 | | - :width: 33% |
37 | | - :alt: the poker game, with the dominated action eliminated |
38 | | - :align: right |
39 | | - :target: _images/pokerdom2.png |
40 | | - |
41 | | -For example, in the poker game, it is strictly dominated for Fred to |
42 | | -choose Fold after Red. Clicking the next level icon |
43 | | -removes the dominated action from the game display. |
44 | | - |
45 | | -The tree layout remains unchanged, including nodes which can only be |
46 | | -reached using actions which have been eliminated. To compress the tree |
47 | | -to remove the unreachable nodes, check the box labeled |
48 | | -:guilabel:`Show only |
49 | | -reachable nodes`. |
50 | | - |
51 | | -For this game, no further actions can be eliminated. In general, |
52 | | -further steps of elimination can be done by again clicking the next |
53 | | -level icon. The toolbar keeps track of the number of levels of |
54 | | -elimination currently shown; the previous level icon moves up one |
55 | | -level of elimination. |
56 | | - |
57 | | -.. image:: screens/pokerdom3.* |
58 | | - :width: 33% |
59 | | - :alt: the poker game, with only reachable actions shown |
60 | | - :align: right |
61 | | - :target: _images/pokerdom3.png |
62 | | - |
63 | | -The elimination of multiple levels can be automated using the fast |
64 | | -forward icon , which iteratively eliminates dominated actions until no |
65 | | -further actions can be eliminated. The rewind icon restores the |
66 | | -display to the full game. |
67 | | - |
68 | | - |
69 | | - |
70 | | -Dominated strategies in strategic games |
71 | | ---------------------------------------- |
72 | | - |
73 | | -The dominance toolbar operates in strategic games in the same way as |
74 | | -the in the extensive game. Strategies can be eliminated iteratively |
| 8 | +can be used to investigate the structure of dominated strategies. |
| 9 | +Strategies can be eliminated iteratively |
75 | 10 | based on whether they are strictly or weakly dominated. |
76 | 11 |
|
77 | 12 | .. image:: screens/pddom1.* |
@@ -106,3 +41,8 @@ thick, solid line. |
106 | 41 |
|
107 | 42 | Clicking the next level icon removes the strictly dominated strategies |
108 | 43 | from the display. |
| 44 | + |
| 45 | +The elimination of multiple levels can be automated using the fast |
| 46 | +forward icon, which iteratively eliminates dominated actions until no |
| 47 | +further actions can be eliminated. The rewind icon restores the |
| 48 | +display to the full game. |
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