Agreed. I was initially hesitant because you said "the model doesn't have enough detail" so I was checking to see if there was a response along the lines of "the model would necessarily fail to represent X" that you would bring up. Anyways, I have in fact discovered a truly marvelous model, but the margin is too small to contain it...

Fortunately, though, URL links are big enough to fit in the margin! http://www.gliffy.com/go/publish/6135045

For the purposes of the model itself you should, of course, ignore all of the suggestively named LISP tokens, except the labels (ALLCAPS) on the outgoing edges of nodes in the same information set (as these tell you which actions are "the same action"). In other words, the actual "model" consists only of:
(1) the nodes
(2) the directed edges
(3) the information set arrows (an equivalence relation)
(4) the identities of arrows out of the same information set (i.e. an equivalence relation on those arrows).
(5) the probabilities associated with a chance node
(6) the values inside the square boxes (utilities)

In the game as I've presented it, the optimal strategy is clearly to:
- always GIVE when Omega asks you
- if for some reason you happened to CALCULATE, you still GIVE after that (also I think you would be well-advised to run a full re-check of all of your AI subsystems to work out why you decided to CALCULATE. Hopefully it was just a cosmic ray ^_~)