+1 for this.

Just be transparent and honest with your Team.

Explain to them how the actual budget is out of your direct control. However, also explain what knobs you and your IC can influence (for example being more visible with your Team/IC's accomplishments at an organizational level).

Also many companies have a "flight risk" box, when calculating raises. Explain to your IC's that you can hit this checkbox (if the IC wants), but it's pretty much a onetime use button.

Don't be afraid to rock the organizational boat. They won't hold it against you, as you're just doing your job. Your goal, first and foremost, is to get the most you can out of your Team and money is a good motivator.

If you need other "cheap" motivators:

• have the Team take some time off (paid or unpaid) and watch/stream a movie, with the mic on. Encourage people to trash talk the movie. If you're in I.T. Office Space is a classic.
• for ~$40 / year, you can get a subscription to Boardgame Arena. Only one person needs a paid account (so they can create games and invite people). It's all online and they have quiet a selection of games to choose from. King of Tokyo is one of our favorites.
• Introduce "Fantastic Friday": this is a bit controversial with upper management, but works great with my Teams in the past. Basically, reserve a Friday (bi-weekly/monthly) where your Team can explore whatever topics they want as long as they've already finished their current workload. Usually, that disclaimer isn't necessary, as people will usually want to get their normal work done. The pitch for upper management (if they ask) is that Fantastic Friday is a tool (ie: a canary in the coalmine) to help the Team create accurate estimates and deliver with more reliability. If they over commit, then that Fantastic Friday can be repurposed as a day to "catch-up" (while the Team can understand/refocus on why they didn't get a Fantastic Friday and pivot accordingly). Furthermore, Fantastic Friday was often used to explore more "outside the box" ideas that actually boosted the Team/companies productivity, but we would not have normally persuded because it was outside our current task's scope.

edit: added more about Fantastic Friday and fix grammar.

Yep, it makes sense when you consider the real nature of management and why it actually exists.

A rich man starts a company. He hires 12 people under him. He's working a bit harder than he'd hoped, he's constantly fielding questions and such but all is well. He needs to hire two more people. This is too many for him to manage directly, so he appoints two people to manage the other twelve as two teams of 6. All is well again.

They expand up to 30 people and suddenly they find the two managers are too stretched again! So another manager has to be introduced. When the company is over about 150 people, we even need multiple layers of management to keep this whole thing afloat as suddenly there are too many managers reporting to the founder or to the managers.

Yet at no point does the person who owns the company agree to give up any real control. If someone sets a budget he doesn't like, he gives that control of the budget to someone else. Everyone in that hierarchy is acting on behalf of the owners under this arrangement.

The managers are just sat there with the mandate to make employees do more work under ever-increasing resource constraints, in the name of profit maximisation.

The management hierarchy functions as little more than a way of getting the owner's instructions down to the employees by people who can interpret them as such, and to feed issues back to whatever level has the ability to deal with them (or declare them not an issue, as is often the case).