Game Theory Dominated Strategy
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Strictly Dominated Strategy
When a player is better off switching away from a strategy no matter what the other player does, we say that is a strictly dominated strategy.
Strictly meaning in all cases.
Dominated meaning there is a better option.
In other words that strategy is always worse.
Eliminate!
We can totally eliminate a strictly dominated strategy.
Example: Dandelion Pty Ltd are planning their ad campaign vs their main competitor FruitBasket.
The ad campaign can be Funny (making people laugh while giving their message), Straight (just saying how good they are) or Aggressive (why the opposition is bad).
Of course FruitBasket may choose whatever strategy they want as well.
Based on experience Dandelion see these benefits:
| Dandelion | ||||
| Funny | Straight | Aggressive | ||
| FruitBasket | Funny | 14, 8 | 2, 10 | 8, 8 |
| Straight | 7, 4 | 4, 8 | 7, 6 | |
| Aggressive | 0, 20 | 3, 18 | 9, 0 | |
In other words, if both of them choose Funny ads the result is "14, 8" meaning FruitBasket gets a beneift of 14 and Dandelion gets 8. And so on.
Looking at Dandelion's Straight vs Aggressive choice:
- 10 is better than 8 (Straight is better)
- 8 is better than 6 (Straight is better)
- 18 is better than 0 (Straight is better)
So for all cases Dandelion is better off using Straight instead of Aggressive style. So we can get rid of the whole Aggressive column:
| Dandelion | |||
| Funny | Straight | ||
| FruitBasket | Funny | 14, 8 | 2, 10 |
| Straight | 7, 4 | 4, 8 | |
| Aggressive | 0, 20 | 3, 18 | |
This makes decisions easier!
We may get lucky and find more than one such case. Let us see if there are any more in our example.
Example: Dandelion Pty Ltd continued
We have (so far):
| Dandelion | |||
| Funny | Straight | ||
| FruitBasket | Funny | 14, 8 | 2, 10 |
| Straight | 7, 4 | 4, 8 | |
| Aggressive | 0, 20 | 3, 18 | |
Looking at FruitBasket's Straight vs Aggressive strategies:
- 7 is better than 0 (Straight is better)
- 4 is better than 3 (Straight is better)
So we can eliminate the bottom row:
| Dandelion | |||
| Funny | Straight | ||
| FruitBasket | Funny | 14, 8 | 2, 10 |
| Straight | 7, 4 | 4, 8 | |
Now looking at Dandelion's Funny vs Straight strategies:
- 10 is better than 8 (Straight is better)
- 8 is better than 4 (Straight is better)
And we get this:
| Dandelion | ||
| Straight | ||
| FruitBasket | Funny | 2, 10 |
| Straight | 4, 8 |
And now for FruitBasket Straight wins:
| Dandelion | ||
| Straight | ||
| FruitBasket | Straight | 4, 8 |
So Dandelion's best choice is a Straight ad campaign, and if FruitBasket is rational they will also choose Straight.
(Note: it won't often work out so neatly, but there are other things we can do to find an optimal choice.)
Wow! In this case we got all the way down to a single best strategy.
Interestingly it does not matter what order we eliminate the strategies we still end up with the same result.
Eliminating more than one strategy this way is called Iterative Elimination of Strictly Dominated Strategies (IESDS), with "iterative" meaning doing the process again.