Open this lesson in your favourite AI. It'll walk you through the why, explain the demo, and quiz you on the try-it list.
Eliminating one dominated strategy sometimes exposes another strategy as now-dominated in the smaller game. Repeat. Sometimes the game collapses to a single strategy profile — and that profile is often the 'solution' to the game without ever mentioning Nash equilibrium. Iterated elimination is the first real solution concept you'll meet, and every time you use it you're quietly invoking common knowledge of rationality from the previous lesson.
Start from the game . Remove strictly dominated strategies for every player simultaneously, producing . Do it again on to get . Keep going until nothing can be removed; the fixed point is the set of iteratively un-dominated strategies:
# A tiny demo: a 3x3 game that reduces to a single profile.
# Rows: U, M, D. Columns: L, C, R. Payoffs are (Row, Col).
payoffs = {
("U","L"): (3,0), ("U","C"): (0,2), ("U","R"): (0,3),
("M","L"): (2,1), ("M","C"
Use these three in order. Each builds on the one before.
Explain iterated elimination of strictly dominated strategies in plain English — what am I actually doing and why is it safe?
Walk me through a 3x3 example where two rounds of elimination produce a unique prediction, showing the reasoning round by round.
Some games are 'dominance-solvable' (iterated elimination gives a unique answer) and some aren't. What structural properties of a game make it dominance-solvable, and why is rationalizability a natural next concept when it isn't?