Game Theory · GT-03
Before you solve a game, throw out every move that can never be the best one.
A solution technique where you repeatedly strike out any strategy that is always worse than another available strategy, regardless of what opponents do — narrowing the game down step by step until only sensible choices remain, sometimes to a single outcome.
A standard technique in classical game theory, used to simplify games before searching for Nash equilibria; formalized alongside the broader von Neumann–Morgenstern framework (1944).
The Mechanism
A 3-option pricing game, reduced round by round
Each round removes a move nobody should ever play — not because it's bad against one specific rival action, but because it's bad against every rival action. Three rounds of elimination can collapse a seemingly complex game down to one predictable outcome.
01 · ELIMINATE, DON'T SOLVE DIRECTLY
A different entry point than searching for equilibrium
Rather than immediately hunting for a Nash equilibrium across the full strategy space, this method first discards options that are strictly worse than some other option no matter what — shrinking the problem before you ever have to reason about what the opponent believes or will do.
02 · ITERATION MATTERS
Removing one dominated strategy can create new ones
The word 'iterated' is doing real work: eliminating a strategy for Player A can make a previously-sensible strategy for Player B newly dominated, once A's discarded option is off the table. You repeat the process, round by round, until no more strategies can be removed.
03 · SOMETIMES IT SOLVES THE WHOLE GAME
A game is 'dominance solvable' when this reduces it to one outcome
In the cleanest cases, iterated elimination whittles the entire game down to a single surviving strategy profile — which is automatically the unique Nash equilibrium. Most real games aren't this clean, but even a partial reduction meaningfully narrows what you need to analyze further.
Where It Fails / Inversion
Where it fails / inversion
This method assumes every player is not just rational, but confidently expects every other player to also be rational, and to expect that of each other, recursively, all the way down — a much stronger and more fragile assumption than it first appears. If any player might be irrational, mistaken, or simply distrustful that the others are being fully rational, the elimination chain can break at any link, and the "obvious" surviving outcome may never actually be reached.
This is precisely the failure mode economists point to in some experimental results (like certain auctions and coordination games), where real participants stop the elimination process early because they aren't confident enough in everyone else's rationality to trust the later rounds.
How To Use It
Worked example · simplifying a hiring negotiation
A candidate is deciding among three counter-offer strategies: aggressive, moderate, or passive. Aggressive risks losing the offer outright and is dominated by moderate in every plausible employer response. Once aggressive is off the table, the employer's "lowball" response becomes dominated by a "fair opening offer" response, since lowballing only made sense as a hedge against candidate aggression. Two rounds of elimination collapse a seemingly open negotiation to a much narrower, more predictable range.
Doing this explicitly before a negotiation — walking your own dominated options off the table first — sharpens your actual decision to the few moves that could plausibly be optimal.
How to use it
When a decision space feels overwhelming, don't try to evaluate every option against every possible response at once. First pass through and cut anything that's worse than some other option no matter what happens — then repeat on what's left. You'll often find the 'real' decision is much smaller than it first appeared.
See Also