Super weak isomorphism of extensive games

It is well known that the normal form suffices to determine some but not to determine all sequential equilibria of a game in general. How much more structure does so? In this addendum to Casajus [Casajus, A., 2003. Weak isomorphism of extensive games. Mathematical Social Sciences 46 (3) 267-290.], we suggest the concept of super weak isomorphism (SWI) as an attempt to answer this question. In contrast to weak isomorphism, SWI is not sensitive to the structure of the chance mechanism and the assignment of payoffs to the individual terminal nodes. Yet, sequential equilibrium remains invariant under SWI, i.e. the structural features preserved by SWI already determine sequential equilibrium. In addition, SWI is generically equivalent to isomorphism of the agent normal form for a larger set of games than weak isomorphism.