From the Advisory Editor:

The authors don't seem to get it. They claim that 30 years of game theory are wrong, and that they
are providing a new approach.  This could be interesting and exciting. But they certainly don't do
any kind of analysis showing where game theory has gotten it wrong up to now. Instead, we get the
observation that what happens in the infinite case cannot always be extrapolated from the finite
case.  While this is certainly true, it certainly gives the reader no insight as to what went wrong
(as far as the authors are concerned) in this case.

Next, the authors try to make an argument that there should be no utility for an infinite play of
the game.  I find this argument unconvincing, to say the least.  First, it is seems based on an
intuition that utilities should be computable.  This is a reasonable intuition, but then it must be
taken far more seriously, and we should talk about computable infinite games.  It might then be
reasonable to define a general notion of infinite game (with utility), and consider a computable
restriction of it.  (Just as we now define languages and consider the subclass of computable
languages.)  I would have also expected a restriction to utilities themselves as being computable
(for example, there is a notion of computable real number, originally defined by Turing, that might
be relevant here).  But that concern doesn't arise in the paper either.  Moreover, in an infinite
game where utilities are attached only to finite leaves, there might still be infinitely many
leaves, and the assignment of utilities to leaves might not be computable.  Finally, it may well be
the case that computable utilities could be attached to infinite paths; we could have a computable
limit of finite processes.  Bottom line: if there is a concern about computability, it must be taken
*much* more seriously.

The authors' only example of when the utility doesn't exist involves a case where utilities are
infinite. This issue has nothing to do with computability, but shows that the problem arises with
*unbounded* utilities. In the Shubik paper, as the authors point out, there is a restriction to
"limited bankrolls". Restricting to bounded utilities is a standard assumption in game theory.
Suppose that we bounded utilities.  Would there be any problem assigning utilities to infinite
paths, from the authors' point of view? Suppose that we allow utilities that are positive infinity
(as well as finite reals), and then take the expected utility of a strategy that gives a utility of
infinity with positive probability to be infinite. It would be easy enough to extend all the
standard definitions to this setting.  If we did that, would that give the same solutions to the
escalation game that the authors get in this paper (without needing to go through coinduction)?

To summarize: the authors claim that they have a new tool to study infinite games, namely
coinduction, and they claim that the old tools give the wrong answer. I could imagine that a paper
that made and proved this claim in a convincing way would be of great interest to game theory.  This
paper does nothing of the kind.  If the authors want to write such a paper, they need to present a
much more careful analysis of what they think goes wrong in the standard game theory arguments,
examine whether the issue is purely one of dealing with unbounded utilities (i.e., unbounded
bankrolls), and justify more carefully the need for undefined utilities.