I used to come up with long, complicated narratives to explain to estate agents why I was only willing to pay a certain amount for a flat they showed me that I wanted to rent: I couldn't afford it, the carpets were old, the living room was smaller than expected, etc., etc. Then one day it struck me that none of this had any point.
The estate agent wants you to get the flat – they get paid a commission for each successful tenant they match to a landlord. The higher the rent the more they get, but this difference isn't very significant. Usually the agent gets the equivalent of a months rent, so if the rent is 2000 GBP / month they get 2000 GBP, and if you negotiate it down to 1900 GBP / month they get 1900 GBP. That's a 100 GBP difference to them, but over a year 1200 GBP to you and the landlord. So just make an offer you are happy with, don't explain too much, and get it over with. The landlord makes the final call, and they don't care about your complicated narratives.
When I first joined a big company, I tended to see it as one big monolith. It took me several months to realize that organizations are not monoliths where everyone has common interests. Every person in the organization has their own incentives. A successful organization will align the incentives of the people in it with the broader organization maybe 50% of the time.
Example: Negotiations with recruiters. It's common to give long narratives about why you need more money when negotiating a job offer. Skip the narratives about how smart you are et al., the recruiter doesn't care. Also skip trying really hard to seem smart and sophisticated with perfect punctuation in your emails, they don't care and won't tell whoever your manager will be about how you don't use the Oxford comma.
Speak to their incentives. They are given a bonus for each hire, but also have a fixed pool of raises and signing bonuses to give out. Either make a stronger case you will walk away (be reasonably polite and you will be fine), or even better, ask them if there's anything you can do to get hired at a more senior position. Your recruiter gets paid more the more senior you are, although their ability to influence this is very limited. However they can do small things like suggesting you get a re-interview for that design interview where the interviewer thought you didn't meet the staff engineer criteria.
Help them help you, talk about how you have other offers that pay better, be polite, they won't mind. They'd like you to get the job, the incentives are aligned here. Don't talk too much about how inspiring the company's values are and how you love the company's products to your recruiter or interviewers. They don't care. Your recruiter has a million other calls to make, your interviewer is still worrying about that project deadline they are going to miss.
The cashier in a supermarket will rarely try to scam you by charging you twice for the same items. After all, even if they did that, the extra money you pay doesn't go to them, it goes to the owner of the supermarket. The only time I've heard of such a scam happening was in a small family-run convenience store. As you might expect, in this case the cashier was also the owner, and so benefited by inflating the customer's bill.
This is the principal-agent problem. The principal (landlord, company shareholders, supermarket owners respectively in the examples above) employs the agent (estate agent, recruiter, cashier respectively) to do a job for them. But sometimes the incentive of the agent and the principal don't align. The fact that the incentives don't align sometimes works against you, but it can also work in your favour.
Speak to incentives of the agent, not the principal.
You're CEO of company X, being considered for acquisition by company Y. In your pitch to the CEO of company Y, you spend all your time talking about how you could increase shareholder value with the acquisition. Bad idea. The CEO's incentives don't perfectly align with the shareholders'. Shareholders care about return on their investment in the company, so they may be willing to decline the acquisition if the return doesn't seem worth it. The CEO, on the other hand, also cares about other things: like the size of the company. The bigger the company, the higher the CEO's prestige. Speak to their incentives.