Dominated strategy
A move that's never worth playing because another always does at least as well.
What it means
A strategy that yields a payoff no greater than some other available strategy against every possible choice by opponents, and strictly less against at least one. Rational players should never use strictly dominated strategies, and removing them can simplify a game — sometimes solving it entirely through iterated elimination. The concept underpins the logic of dominance solvability and clarifies why certain options can be discarded before any deeper strategic reasoning. It matters because spotting and deleting dominated strategies is the first tool of game-theoretic analysis, and because real players sometimes fail to eliminate them, revealing limited strategic depth.
Strict versus weak dominance
Strict dominance means a strategy does worse against every opponent choice; weak dominance means it does no better anywhere and strictly worse somewhere. The distinction is not pedantic. Eliminating strictly dominated strategies is order-independent — the surviving set is the same whatever sequence you delete in — and never discards a Nash equilibrium. Eliminating weakly dominated ones is neither: the outcome can depend on deletion order, and a legitimate equilibrium can vanish along the way. Most textbook iterated-dominance results quietly rely on strict dominance for exactly this reason. When an argument leans on weak dominance instead, its conclusions are fragile, and practitioners should treat the elimination as a useful heuristic rather than a theorem.
Iterated elimination and dominance solvability
Deleting a dominated strategy can make a second strategy dominated that was not before, because the opponent's remaining options have shrunk. Repeating the step can unravel a game to a single prediction — dominance solvability. The clearest case is the p-beauty contest: pick a number, and whoever is closest to two-thirds of the group average wins. Any guess above 67 is dominated, then any above 44, and so on, until the only surviving choice is zero. Reaching it requires many rounds of the same reasoning applied to everyone at once. The idea scales from this toy to Bertrand pricing and bargaining, wherever the chain "if they are rational, that option cannot pay, so this one cannot either" runs forward.
What the evidence shows
Experiments find that people eliminate shallowly. In Nagel's beauty-contest study, choices clustered around 33 and 22 — one or two steps of best-response reasoning rather than literal rounds of dominance deletion — well short of the equilibrium of zero, and later work formalized this as level-k or cognitive-hierarchy reasoning, with an average near 1.5 steps. Failure shows up even at a single step. Beard and Beil found that subjects often decline a move that pays them more whenever a second player best-responds, because they doubt the second player actually will. Hanaki and colleagues report that fluid intelligence predicts who eliminates correctly, yet individual cognitive skill explains only a small share of the failures; the structure of the decision environment matters at least as much.
Why elimination breaks down
Discarding a dominated strategy for yourself needs only your own rationality. Discarding one through iteration needs you to trust the rationality of others, and their trust in yours, up the chain. Each added round demands a stronger assumption about common knowledge of rationality, and real players' confidence decays quickly. When the payoff gap between the dominated option and its rival is small, or when the dominated choice happens to be the safe one under uncertainty about opponents, players knowingly keep it. This is why dominance is a dependable guide for a lone decision-maker but a weak predictor of group outcomes: the theory assumes a tower of mutual rationality that people do not actually climb.
Examples
If pricing high earns you less than pricing low no matter what a rival does, pricing high is dominated and should be dropped.
On a multiple-choice test with no penalty for wrong answers, leaving a question blank is dominated: a guess scores the same when wrong and better when right.
If the toll road costs nothing extra on your season pass and is never slower than the free route, taking the free route is dominated — no traffic pattern makes it the better call.
In a second-price sealed-bid auction, bidding above your true value is dominated: it only wins auctions you would rather lose, while never lowering the price you pay when winning was already worthwhile.
A suspect offered a deal where confessing brings a lighter sentence than silence no matter what an accomplice does holds a dominated option in staying silent — the engine of the prisoner's dilemma.
First described in Game theory; von Neumann & Morgenstern (1944).
Key references
- Hanaki, N., Jacquemet, N., Luchini, S., & Zylbersztejn, A. (2016). Fluid Intelligence and Cognitive Reflection in a Strategic Environment: Evidence from Dominance-Solvable Games. Frontiers in Psychology, 7, 1188. doi.org/10.3389/fpsyg.2016.01188
- Camerer, C. F., Ho, T.-H., & Chong, J.-K. (2004). A Cognitive Hierarchy Model of Games. Quarterly Journal of Economics, 119(3), 861-898. doi.org/10.1162/0033553041502225
- Nagel, R. (1995). Unraveling in Guessing Games: An Experimental Study. American Economic Review, 85(5), 1313-1326. ideas.repec.org/a/aea/aecrev/v85y1995i5p1313-26.html
- Beard, T. R., & Beil, R. O. (1994). Do People Rely on the Self-Interested Maximization of Others? An Experimental Test. Management Science, 40(2), 252-262. doi.org/10.1287/mnsc.40.2.252
- von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press. press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior