The example of the Rubinstein bargaining model suggests that you could make players alternate offers and introduce exponential temporal discounting. An equal split isn't logically necessary in this case: a player's payoff will likely depend on their personal rate of utility discounting, also known as "impatience", and others' perceptions of it. The search keyword is "n-person bargaining"; there seems to be a lot of literature that I'm too lazy and stupid to quickly summarize.