It also is extremely puzzling that in this posting you are saying that NBS and KSBS are not Pareto optimal when in the last posting, it seemed that they were Pareto by definition. What has changed?

You explained that yourself: they are Pareto Optimal in a single game, but are not when used as sub-solutions to a game of many parts.

Well, you seem to have understood everything pretty well, without the need for extra information. And yes, I know about comparing utility functions, and yes I know about Rawl's Veil of Ignorance, and its relevance to this example; I just didn't want to clutter up a post that was long enough already.

The insistence on dynamic consistency is to tie it in with UDT agents, who are dynamically consistent. And the standard solutions to games of incomplete information do not seem to be dynamically consistent, so I did not feel they are relevant here.

The first point is that your μ factor, as well as U1 and U2, are not pure real numbers, they are what a scientist or engineer would call dimensioned quantities.

U1 and U2 are equivalent classes of functions from a measurable set of possible worlds to the reals, where the equivalence classes are defined by affine transformations on the image set. μ is a functional that takes an element of u1 of U1 and an element u2 of U2 and maps them to a utility function equivalence class U3. It has certain properties under affine transformations of u1 and u2, and certain other properties if U1 and U2 and replaced with U1' and U2', and these properties are enough to uniquely characterise μ, up to a choice of elements in the real projective line with some restrictions.

But U1+μU2 is an intuitive summary of what's going on.