The outside option is often referred to as the BATNA: Best Alternative to a Non-Negotiatied Agreement.

Outside options influence the surplus parties can get in a negotiation because, if any party's outside option is worse than what it gets from a proposed deal, that party will walk away from negotiations.

Manipulating the parties' outside option (for instance, through a break-up fee) can help mitigate the holdup problem.

One party can capture a larger share of the surplus in a negotiation, by increasing its bargaining power.