Suppose at a restaurant my friend ordered \$30 worth of pizza, and I ordered \$20. The restaurant is having a promotion so that we could get the second order at half price (the second order can't be more expensive than the first one), so we should pay \$30+\$20/2=\$40. How much should we pay?
I've heard of the Talmud division, but here we're claiming debts rather than incomes, so I'm not sure that the concept applies. Besides if we do the Talmud division then the person who placed the first order always have to pay the full price, which doesn't seem fair. Is there any equilibrium state here?
Thanks!
There are some hidden assumptions in the question, namely whether or not the orders were made expecting to get a discount from the promotion.
In the simple case where both orders were made ignorant of the promotion (and the waitstaff just tells you that there will be a discount), then your friend is willing to pay \$30 and you are willing to pay \$20. If you were each eating separately, that is what you would pay. The restaurant is giving you a \$10 bonus, which neither of you would get if you were dining alone. Hence it seems fair to split the bonus equally.
However, things get more complicated if one or both of you were already expecting to get some part of the discount. For example, suppose you would have ordered nothing at all without the promotion, but are willing to pay a maximum of \$10 for pizza (which you believe to be overpriced). Then, in your mind, there is no bonus.
Sadly, once the orders have been placed it is too late to sort these issues out; the best time to decide on the discount is before the order has been placed. There are various methods involving bidding that would resolve the matter as well, provided you and your friend are willing to swap dinners for the right price.