Imagine a game where one strategy is best no matter what your opponent does. You don’t need to predict their behavior, guess their intentions, or outthink them. You just pick the dominant strategy and you’re done.
This is the simplest situation in game theory—and when you have a dominant strategy, your decision becomes trivial. Let’s understand this powerful concept.
What is a Dominant Strategy?
A dominant strategy is a strategy that gives you a better outcome than any other strategy, regardless of what your opponents do.
what others do"] B --> C{If opponent
does X?} B --> D{If opponent
does Y?} B --> E{If opponent
does Z?} C --> F["Dominant strategy
is still best"] D --> F E --> F F --> G["Easy decision!
Always play it"] style A fill:#4c6ef5 style B fill:#51cf66 style F fill:#51cf66 style G fill:#51cf66
The beauty: You don’t need to predict what others will do. Your choice is independent of theirs.
The catch: Dominant strategies are relatively rare. Most games don’t have them.
A Simple Example: The Confession Game
You and a partner are arrested. You’re each offered a deal (the Prisoner’s Dilemma structure):
| Partner: Silent | Partner: Confess | |
|---|---|---|
| You: Silent | 1 year, 1 year | 10 years, 0 years |
| You: Confess | 0 years, 10 years | 5 years, 5 years |
Let’s check if you have a dominant strategy:
Case 1: Partner stays silent
- If you stay silent: 1 year
- If you confess: 0 years
- Confessing is better ✓
Case 2: Partner confesses
- If you stay silent: 10 years
- If you confess: 5 years
- Confessing is better ✓
Confessing is a dominant strategy—it’s better regardless of what your partner does.
Silent: 1 year"] B1 --> B2["✓ Confess wins"] C --> C1["Confess: 5 years
Silent: 10 years"] C1 --> C2["✓ Confess wins"] B2 --> D["Confess is
DOMINANT STRATEGY"] C2 --> D style A fill:#4c6ef5 style B2 fill:#51cf66 style C2 fill:#51cf66 style D fill:#ffd43b
And here’s the key: Your partner has the same dominant strategy. You’ll both confess and both get 5 years—even though you’d both be better off staying silent (1 year each).
Dominant vs. Dominated Strategies
Two related concepts:
Dominant Strategy
A strategy that’s better than all your other strategies, no matter what opponents do.
Dominated Strategy
A strategy that’s worse than another strategy you have, no matter what opponents do.
If you have a dominant strategy: Play it!
If you have dominated strategies: Never play them—eliminate them from consideration.
✓ PLAY THIS"] C --> C1["Sometimes good
Depends on context"] D --> D1["Never best
❌ ELIMINATE THESE"] style A fill:#4c6ef5 style B fill:#51cf66 style B1 fill:#51cf66 style C fill:#ffd43b style D fill:#ff6b6b style D1 fill:#ff6b6b
A Business Example: Advertising
Two competing companies must decide whether to advertise:
| Competitor: Advertise | Competitor: Don’t Advertise | |
|---|---|---|
| You: Advertise | $5M profit, $5M profit | $12M profit, $2M profit |
| You: Don’t Advertise | $2M profit, $12M profit | $8M profit, $8M profit |
Your analysis:
If competitor advertises:
- You advertise: $5M
- You don’t: $2M
- Advertising is better ✓
If competitor doesn’t advertise:
- You advertise: $12M
- You don’t: $8M
- Advertising is better ✓
Advertising is your dominant strategy.
By symmetry, it’s also your competitor’s dominant strategy. Result: Both advertise and get $5M each—when you could have both not advertised and gotten $8M each!
(Could have earned $8M
if both didn't advertise) style Y fill:#ff6b6b style C fill:#ff6b6b
This is why advertising can be a race to the bottom—even though everyone would be better off with less advertising, each firm has an incentive to advertise.
When Dominant Strategies Lead to Bad Outcomes
Having a dominant strategy makes your decision easy, but it doesn’t guarantee a good outcome:
The Tragedy of Dominant Strategies
When everyone has a dominant strategy, they’ll all play it—but the result can be bad for everyone:
Examples:
- Prisoner’s Dilemma: Both confess (5 years each) instead of staying silent (1 year each)
- Advertising wars: Both advertise ($5M each) instead of no ads ($8M each)
- Arms races: Both arm (costly stalemate) instead of peace (cheaper security)
- Doping in sports: Everyone dopes (health risks, no advantage) instead of clean competition
Equilibrium] --> B{Good outcome?} B -->|Sometimes| C["Both have dominant strategy
that benefits all"] B -->|Often Not| D["Both follow dominant strategy
End up worse than cooperation"] C --> C1["Efficient outcome
Everyone happy"] D --> D1["Prisoner's Dilemma
Tragedy of Commons"] style A fill:#4c6ef5 style C fill:#51cf66 style C1 fill:#51cf66 style D fill:#ff6b6b style D1 fill:#ff6b6b
Iterative Elimination of Dominated Strategies
Sometimes you don’t have a dominant strategy, but you can still simplify the game by eliminating dominated strategies:
The process:
- Remove any strategies that are dominated
- In the simplified game, look for newly dominated strategies
- Repeat until no more strategies can be eliminated
- See what’s left
Example:
| Opponent: Left | Opponent: Middle | Opponent: Right | |
|---|---|---|---|
| You: Up | 5, 1 | 3, 2 | 1, 4 |
| You: Middle | 4, 3 | 4, 1 | 3, 2 |
| You: Down | 3, 4 | 5, 3 | 2, 1 |
Step 1: Do you have a dominant or dominated strategy?
- Up vs Middle: Up gives 5 vs 4 (Left), 3 vs 4 (Middle), 1 vs 3 (Right)
- Middle dominates Up when opponent plays Middle or Right
- But Up dominates Middle when opponent plays Left
- Neither is strictly dominated
Let’s check Down:
- Down vs Middle: Down gives 3 vs 4 (Left), 5 vs 4 (Middle), 2 vs 3 (Right)
- Down is better when opponent plays Middle, but worse on Left and Right
No strictly dominated strategies for you.
Step 2: Does opponent have dominated strategies?
For opponent’s perspective (their payoffs):
- If you play Up: They get 1 (Left), 2 (Middle), 4 (Right)
- If you play Middle: They get 3 (Left), 1 (Middle), 2 (Right)
- If you play Down: They get 4 (Left), 3 (Middle), 1 (Right)
Comparing Left vs Right for opponent:
- When you play Up: Right (4) > Left (1)
- When you play Middle: Left (3) > Right (2)
- When you play Down: Left (4) > Right (1)
Left dominates Right in 2 out of 3 cases—not strictly dominated.
Eliminate them"] B1 --> C[Round 2] C --> C1["In reduced game,
find newly dominated strategies"] C1 --> D[Repeat] D --> E["Until no more
can be eliminated"] E --> F["Remaining strategies
are rational choices"] style A fill:#4c6ef5 style B1 fill:#ffd43b style C1 fill:#ffd43b style F fill:#51cf66
Real-World Examples of Dominant Strategies
1. Always Bid Your True Value in Second-Price Auctions
In a Vicksburg (second-price) auction, the highest bidder wins but pays the second-highest bid.
Bidding your true valuation is a dominant strategy:
- Bidding higher doesn’t help (you pay more when you win)
- Bidding lower hurts (you might lose when you could have profited)
2. Telling the Truth (Sometimes)
In certain mechanism designs (like the VCG mechanism), telling the truth about your preferences is a dominant strategy.
3. Vaccination (From Society’s View)
For society as a whole, everyone vaccinating is often dominant—it’s better regardless of what others do (though individuals face different incentives due to free-riding).
4. Taking the Middle Urinal (When Three Available)
In men’s restrooms with three urinals:
- If no one is there: Middle is probably not optimal (leaves no good options for next person)
- Actually, this is NOT a dominant strategy example—it depends on privacy preferences and social norms!
Strategies] --> B[Second-price Auction] A --> C[Truth-telling
in VCG] A --> D[Confession in
Prisoner's Dilemma] B --> B1["Bid true value
Always optimal"] C --> C1["Honest reporting
Always best"] D --> D1["Confess
Always better"] style A fill:#4c6ef5 style B1 fill:#51cf66 style C1 fill:#51cf66 style D1 fill:#ff6b6b
Why Dominant Strategies Are Rare
Most strategic situations don’t have dominant strategies because:
1. Your best choice usually depends on what others do
In coordination games, matching matters. In competition, responding to opponents matters.
2. Trade-offs exist
Different strategies are good in different situations. There’s no “always best” option.
3. Games are complex
Real-world situations have many players, many strategies, and context-dependent payoffs.
When dominant strategies do exist:
- The game is usually relatively simple
- There’s strong strategic alignment (everyone wants the same thing) or strong conflict (Prisoner’s Dilemma)
on others' actions"] C --> D["Need to predict
or react strategically"] E[Games with
Dominant Strategy] --> F["Easy decision
Just play it"] F --> G["But may lead to
bad equilibrium"] style A fill:#ffd43b style B fill:#ffd43b style E fill:#51cf66 style F fill:#51cf66 style G fill:#ff6b6b
The Strategic Implications
If You Have a Dominant Strategy:
✓ Play it—your decision is simple ✓ You can predict opponents with dominant strategies will play them too ✓ Be aware the outcome may still be suboptimal for everyone
If You Don’t Have a Dominant Strategy:
✓ Check if any of your strategies are dominated and eliminate them ✓ Consider what opponents will do ✓ Look for Nash Equilibria ✓ Think about best responses to likely opponent strategies
If You’re Designing a Game or System:
✓ Consider giving participants dominant strategies toward desired behaviors ✓ Be aware that dominant strategies can lead to Prisoner’s Dilemmas ✓ Design incentives so that dominant strategies align with good outcomes
The Takeaway
Dominant strategies make decisions easy: When you have one, you don’t need to predict opponents’ behavior—just play your dominant strategy.
But easy doesn’t mean good: The Prisoner’s Dilemma shows that when everyone follows their dominant strategy, the outcome can be terrible for everyone.
Recognize them in the wild:
- Confessing when interrogated
- Advertising when competitors advertise
- Arming when adversaries might arm
- Bidding true value in second-price auctions
The wisdom: Having a dominant strategy simplifies your decision, but doesn’t guarantee happiness. Sometimes the “rational” choice (following your dominant strategy) leads to outcomes where everyone loses.
This is part of our Game Theory Series. Dominant strategies are the simplest case in game theory—when you have one, your choice is obvious. But as the Prisoner’s Dilemma shows, individually rational dominant strategies can lead to collectively terrible outcomes.