Investigating dominated strategies#
Selecting toggles the appearance of a toolbar which can be used to investigate the structure of dominated strategies. A Hide strategies which are dropdown at the left of this toolbar selects whether strategies are considered dominated when they are strictly dominated, or when they are strictly or weakly dominated; this defaults to strictly. Strategies can then be eliminated iteratively based on whichever of these two notions is selected.
When the dominance toolbar is shown, the strategic game table contains indicators of strategies that are dominated according to the selected notion. In the prisoner’s dilemma, with the dropdown set to strictly, 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.
Setting the dropdown to strictly or weakly additionally indicates weakly dominated strategies, using the same “X” shape drawn with a thinner, dashed line instead of the thick, solid line used for strict dominance.
To the right of the dropdown, a status readout (for example, All strategies shown or Eliminated 1 level) shows how many rounds of elimination are currently applied, and four buttons step through rounds of elimination one at a time or all at once. Clicking Next round of elimination removes the currently-indicated dominated strategies from the display, advancing one round; Previous round of elimination undoes the most recent round, restoring the strategies it removed. The elimination of multiple rounds can be automated using Eliminate iteratively, which repeats elimination until no further strategies of the selected notion can be eliminated. Show all strategies restores the display to the full game.