An allocation $x^{*}$ is said to have the core property in a game of $N$ players if there is no coalition $S \subseteq N$ that can improve upon $x^{*}$. The core of a game is the set of allocations with the core property.
Now, a coalition $S$ will block an allocation $x$ if there exists a feasible $\widetilde{x}$ such that $\widetilde{x} \succ_{s} x$ for all $s \in S$.
As a practical matter, to determine the core of a cooperative game we usually must compute the allocations that any coalition $S$ will not block (i.e. the allocations that cannot be improved upon). If we denote this allocation as $A_{S}$ then we can write the core allocation $\mathcal{C}$ as $$\mathcal{C} = \bigcap_{S \in 2^{N}} A_{S} $$
Now in any game with more than two players it can be tedious to compute the core.
I am wondering, if I knew the game was a transferable utility game, is there any way to compute the core more efficiently?
This is mostly a question about the consequences of a game being a transferable utility game, and whether this provides any information that is useful to computing the core. Although I am familiar with the definition of transferrable utility, I was never really comfortable with what it's practical implications were for the game.