Payment as part of game semantics

In CL, a semantical object maps each run to a set of possible moves for both players and a currently winning player. One idea would be to replace the latter by payments. I mean, if one uses games as contracts, it makes more sense saying that as a result of our interaction I owe you 10 euro by the end of the year than to say that I lost my contract. As a side effect, it makes possible win/win (or lose/lose) outcomes - I owe you 10 euro by the end of the year, but you owe me 10 dollars by the end of the month. Then again, how to enforce these payments? Sooner or later we must reach some escape hatch for extra-logical enforcement (court?). But I still believe that it may be more useful to come to court asking for 10 euro than asking to make false true.

Also, when going to court, you want to bring some evidence, or witness. So the outcome is not a boolean, but a scheduled flow of expected payments, each annotated with a witness (a non-repudiable pointer to a move that decided this payment). Note that missing a payment must be interpreted as a move as well - and thus modify the outcome. I wonder, if this can be implemented at least in theory, or there is some metacircular recursion ("it's moves all the way down").

PS: http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/199.PDF