Level-k Thinking

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins.

Obviously, picking a number over 50 would be silly. Based on this, picking a number over 25 would be silly. Similarly, picking a number over 12.5 would be silly. Continuing this line of thought, picking any number other than 0 would be silly. These thoughts show the level of thinking of those involved, from level-1 to level-infty.

Level-k thinking analyzes such games. In actual experiments, players never pick 0, which would be suggested by a Nash equilibrium. Instead, they utilize many different levels of thinking.

See also

Nash Equilibrium

This entry contributed by Ed Pegg, Jr.

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Crawford, V. P. "Level-k Thinking, Outguessing and Deception in Games." Jan 2005., J. F. "Non-Cooperative Games." Ann. Math. 54, 286-295, 1951.

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Level-k Thinking

Cite this as:

Pegg, Ed Jr. "Level-k Thinking." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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