The definition of a rationalizable strategy is given in "A Course in Game Theory" by Osborne & Rubinstein on Chapter 4 as Definition 54.1 in the book (which is freely available at books.osborne.economics.utoronto.ca), as a formalization of the intuition that it is a common belief of all players that a player will assign zero probability to choosing a strategy which is not a best response to what he believes to be the strategies of all other players. It turns out that this definition is unsatisfactory for extensive-form games, because there are strategies that are eliminated via backward induction but are rationalizable (and even part of a Nash equilibrium).
Here's the excerpt from the book that really matters to my question: Book Snapshot of the Definition of Rationalizability
I'd like to define the notion of "sequential rationalizability" that corresponds to sequential equilibrium in analogous sense that "rationalizability" corresponds to Nash equilibrium.
My intuition is that the new definition is simply rationalizability plus an extra assumption: It is a common belief of all players (at all states of the game) that a player's "belief" (at an information state where he plays) about the strategies of all other players assigns zero probability to all strategies that are not consistent with his arriving at the information state where he's being.
Notice that this definition requires the "rationalizable set of beliefs" be given for each player at each information set where he plays. This is necessary, because if a belief of a player (at one state) assigns zero probability to a move of another player, then at a(nother) state that is only consistent to that move having already occurred, he is forced to have a different "belief" (that is, he should revise his belief upon realizing that an event he previously believed to be impossible has occurred).
Can you give a definition of this "sequential rationalizability" that is analogous to Definition 54.1 of the book? I've yet to find such an idea in the literature. There are many different ideas people proposed of what sequential rationalizability should be, and some try to derive directly from logical models of the players' behaviors (notice that, on the other hand, Osborne & Rubinstein derives Definition 54.1 as a mathematical formalization that "intuitively follows" from the immediately preceding intuition given in the book before that definition). Please offer a definition that corresponds to (the intution given in the book, plus:) the intuition I've given above.