Level-k thinking in the extensive form
研究了扩展式博弈中的层级k思维，玩家在博弈过程中可能根据对手的思维层级更新信念，并用该概念重新分析已有实验数据。
Abstract Level- k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. Player’s may learn about levels of opponents’ thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level- k player attaches the maximum level- $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> thinking for $$\ell < k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo><</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:math> to her opponents consistent with the information set. We compare our notion of strong level- k thinking with other solution concepts such as level- k thinking in the associated normal form, strong rationalizability, $$\Delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -rationalizability, iterated admissibility, backward rationalizability, backward level- k thinking, and backward induction. We use strong level- k thinking to reanalyze data from some prior experiments in the literature.