Handbook of Game Theory

12.7.3 Initial CBR

We begin with the simplest set of epistemic assumptions that take into account the extensive-form nature of the game, but are still close to strategic-form analysis in spirit.

Following Ben-Porath (1997), we consider the assumption that players are (sequentially) rational and initially commonly believe in (sequential) rationality:

$\begin{array}{l}RICB{R}_i^0=R_i,\\ \begin{array}{ccc}RICB{R}_i^k=RICB{R}_i^{k-1}\text{∩}{B}_{i,\varphi }\left(RICB{R}_{-i}^{k-1}\right)& \text{for}& k<0,\end{array}\\ RICB{R}_i=\underset{k\ge 0}{\text{∩}}RICB{R}_i^k.\end{array}$

  [12.22]

Except for the fact that rationality is interpreted in the sense of Definition 12.24, these epistemic assumptions are analogous to RCBR in simultaneous-moves games, as defined in Eqs. 12.9 and 12.10. Direct restrictions ...