"For now we will only consider transactions that conserve wealth, so our transaction rules will decide how to split up the pot of X+Y total wealth."

Economics is not about redistribution of wealth, it is about human actions that generate -- or destroy -- wealth.

Wealth, in economics, is not a quantity of money, it is some set of valuable goods usable in producing other goods or to be consumed.

In fact, every voluntary transaction by definition creates wealth, because it brings the goods (being transacted) from an individual who values them less to an individual who values them more -- and vice-verse.