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Emile comments on Explicit Optimization of Global Strategy (Fixing a Bug in UDT1) - Less Wrong
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Set aside different preferences, because I have no idea how to deal with that. It seems like just having different source codes makes things very difficult.
You used "1" and "2" as your indexical labels, which come with a very obvious order. But suppose that Omega labeled one agent ♠ and the other agent ♣. If you and your opposite have different source codes, you have no idea how your opposite internally represents the symbol that they received. For example, you certainly have no guarantee that the two of you order these in lexicographically the same way. So how could you possibly coordinate on a tie-breaking strategy?
I'd use alphabetical ordering, and assume my opposite would too. So clubs would come before spades, black before white, etc.
Now, if your opponent doesn't use the same language (or doesn't use a language, only unicode symbols), it almost becomes a game of chance, like "here's an aarvark and a wapiti, the same animals have been shown to some (non-english speaking) Chinese guy, you each get to choose one, if the two of you choose different ones you get a hundred bucks".