Iterated deletion of dominated strategies
Delete dominated strategies, then delete those dominated in what remains, and repeat.
Often misread asRunning the deletions happily to the very end, then being surprised that real people stop two or three rounds in, as if the procedure were a prediction about behaviour rather than a chain of assumptions.
How to see it
Delete what they would never do, then what you would never do given that
First remove every strategy no player would ever use. That makes the game smaller. In the smaller game, options that were worth keeping may now be worthless, so remove those too, and keep going. What is left is what survives everyone reasoning about everyone.
The checkEvery extra round costs another layer of 'and they know that I know', and people run out of layers long before the arithmetic does.
Try itIn the traveller's dilemma, carry the deletions all the way to the bottom and note the round at which you personally stopped believing the other player would follow you down. That number is roughly your own depth of reasoning.
Games that show it
- Teach, distract, then test
- Beauty contest game
- Cournot duopoly
- A dominance-solvable 3x3 game
- Traveller's dilemma
- A zero-sum 2x3 game
Know these first
Leads on to
Easily confused with
Sources
- Nagel, R. (1995). American Economic Review 85(5), 1313-1326.