Dominant Strategy Generator
Some strategies are simply never worth playing: whatever the opponent does, something else does better. Removing them is the first move in solving a game, and the interesting part is that it cascades — once an opponent's option is gone, a strategy that looked reasonable can become dominated in turn. Sometimes this alone settles the game entirely.
What this generator does
Builds a payoff grid and repeatedly removes any strategy that is beaten by another whatever the opponent does, alternating between the two players until nothing more can be removed. It records each removal and reports what survives.
How to use this tool
- Generate a game and look for a row that is beaten by another row in every column.
- Remove it, then look again — the picture has changed.
- Repeat for the columns, and keep alternating.
- Compare what survives with the answer shown.
Understanding the controls
- Row strategies
- Between 2 and 4 choices for the first player.
- Column strategies
- Between 2 and 4 choices for the second player. More options on either side give the cascade more room to run.
- Seed
- Any word reproduces exactly the same game and the same eliminations.
Common use cases
- Teaching iterated elimination with the cascade made visible
- Game theory practice with a verifiable answer
- Showing why the order of elimination does not change the outcome
- Generating problems for a lesson or a problem set
- Setting the same game twice from a seed
How this generator works
Each removal is recorded together with the opponent's options that were still in play at that moment, because that context is part of the claim — a strategy dominated after two columns have gone is not necessarily dominated against the full grid. Domination is strict: better somewhere and never worse. A strategy that merely ties everywhere is left alone, since removing it could discard a genuine equilibrium.
Randomness and fairness
The payoffs are random; the eliminations follow deterministically. A seed reproduces the same game exactly and is therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Strict domination only. Weak domination — never worse but only sometimes better — can be eliminated too, but the result then depends on the order, which is why it is left out.
- Elimination narrows a game and often does not solve it; what survives may still contain several equilibria.
- Two players with one simultaneous move each.
- Pure strategies only; a strategy dominated by a mixture is not detected.
- Games are not stored between visits; seed one you want again.
Privacy and your data
The grid and every elimination are computed on your own device. Neither the game nor your seed leaves the browser.
Related generators
- Nash Equilibrium GeneratorPayoff grids with every pure equilibrium found by testing each cell against every alternative for both players.
- Decision Matrix GeneratorScore options against weighted criteria — with cost and risk counting the right way round, and a check on how solid the answer is.
- Risk Matrix GeneratorScores a risk register on likelihood, impact, detectability and control, so the register is comparable rather than just long.
- Auction Mechanism GeneratorRuns the same private values through a first-price and a second-price auction, proving by enumeration that honest bidding cannot be beaten in the second.