Investigating dominated strategies and actions

Selecting Tools ‣ Dominance toggles the appearance of a toolbar which can be used to investigate the structure of dominated strategies and actions.

Dominated actions in extensive game

In extensive games, the dominance toolbar controls the elimination of actions which are conditionally dominated.

Actions may be eliminated based on two criteria:

Strict dominance

The action is always worse than another, regardless of beliefs at the information set;

Strict or weak dominance

There is another action at the information set that is always at least as good as the action, and strictly better in some cases.

For example, in the poker game, it is strictly dominated for Fred to choose Fold after Red. Clicking the next level icon removes the dominated action from the game display.

The tree layout remains unchanged, including nodes which can only be reached using actions which have been eliminated. To compress the tree to remove the unreachable nodes, check the box labeled Show only reachable nodes.

For this game, no further actions can be eliminated. In general, further steps of elimination can be done by again clicking the next level icon. The toolbar keeps track of the number of levels of elimination currently shown; the previous level icon moves up one level of elimination.

The elimination of multiple levels can be automated using the fast forward icon , which iteratively eliminates dominated actions until no further actions can be eliminated. The rewind icon restores the display to the full game.

Dominated strategies in strategic games

The dominance toolbar operates in strategic games in the same way as the in the extensive game. Strategies can be eliminated iteratively based on whether they are strictly or weakly dominated.

When the dominance toolbar is shown, the strategic game table contains indicators of strategies that are dominated. In the prisoner’s dilemma, the Cooperate strategy is strictly dominated for both players. This strict dominance is indicated by the solid “X” drawn across the corresponding strategy labels for both players. In addition, the payoffs corresponding to the dominated strategies are also drawn with a solid “X” across them. Thus, any contingency in the table containing at least one “X” is a contingency that can only be reached by at least one player playing a strategy that is dominated.

Strategies that are weakly dominated are similarly indicated, except the “X” shape is drawn using a thinner, dashed line instead of the thick, solid line.

Clicking the next level icon removes the strictly dominated strategies from the display.