Two firms decide whether to run an expensive ad campaign. Sometimes one choice pays more than the other no matter what the rival does. When that happens, the decision makes itself.
Dominant and dominated strategies
A strategy is dominant when it beats your alternatives against every move the other player could make. Its opposite, a strictly dominated strategy, should never be played, and spotting one shrinks the game.
In the payoff table, whose number comes first in each cell?
Find the move that always wins
Read down your two rows. If they advertise, you get 3 from advertising versus 1 from not. If they do not, you get 6 versus 4. Advertising wins in both columns.
Eliminate the dominated move
For you, advertising beats not-advertising in every column ( and ), so “do not advertise” is strictly dominated and can be crossed out. By symmetry the same holds for them. What remains is a single cell, , paying , even though both would prefer the they reach by staying quiet. Sound familiar? That tension is the Prisoner’s Dilemma, three lessons from here.
Key idea
If one of your moves pays more than the alternatives against every choice the other player could make, take it and never look back. If a move loses to another against everything, it is dominated: delete it.
A strategy is weakly dominated if another strategy never pays less and pays more against at least one opponent move. Unlike strict dominance, deleting weakly dominated strategies can change which later deletions are possible, so the order can matter.
Check yourself
Sources
- Gibbons, R. (1992). Game Theory for Applied Economists. Princeton University Press.
- Osborne, M. J. (2004). An Introduction to Game Theory. Oxford University Press.