A summary of three types of strategies.
Ask for a little bit more at a time, and keep nibbling away - at small things. Obviously small things accumulate. Airline example:
Airlines usually overbook their seating when possible; on a plane that seats 120, they can sell 122 tickets and just about get away with it, because there is a roughly 3% chance that people don't show up. (Exactly why they oversell I shall explain below.)
Anyways, consider that you're on the plane and they are at capacity. The attendant announces that they need a seat for someone that actually showed up and began offering a seat on the next flight... with compensation of course. So the deal is that you get on the next plane, which leaves tomorrow, and plus a bonus of $100 for your troubles. If you want the offer, you can take it by raising your arm. Nobody took it. Then they increased to $200. And still, nobody budged. Slowly, with $100 at a time, it got to $800. Only then, since you calculate the price to be about fair for your troubles, would you take it.
Should you stop here? No. You should nibble. How?
Since you're getting your flight bumped to the next day, nibble for other benefits.
Nibble: Counter offer for $1000 (increasing your $800 bonus):
There'll be a person to handle your bumped flight. Let's call her Alice.
You: "Could you put me in first class tomorrow? Since I was delayed and all."
Alice: "Well, sure."
You: "I need to stay somewhere tonight, could you put me in a hotel somewhere - I don’t want my parents driving me back to get picked up." (Airlines usually have partnerships with local hotels; for their pilots.)
Alice: "Hmm, okay."
You:"I also have to have to eat, could you give me a food voucher for tonight?"
Alice: "Right, of course."
You: "Also. Someone is supposed to pick me up tonight, could you get car service to drive me home tomorrow night?"
Alice: "I suppose we could."
There. by asking the other side to throw in something small, you have made your offer even better.
Expand your horizon for bargaining. When negotiating salaries and they want to stay firm, ask for vacation. Ask for company car.
Disarming empathy. Offer something low, enough to make you mad. When they counter offer, say this offer is very good, reasonable and the item is worth it. Don’t settle until they give you an ultimatum. Then bargain at other dealers, see if there are better deals.
Why Airlines oversell tickets
From STAT 230
An airline knows that 97% of the passengers who buy tickets for a certain fight will show up on time. The plane has 120 seats.
a) They sell 122 tickets. The probability that more people will show up than can be carried on the fight:
Compare this answer with the answer given by the Poisson approximation.
b) What assumptions does your answer depend on? How well would you expect these assumptions
to be met?
Binomial requires all passengers to be independent as to showing up for the fight, and that each passenger has the same probability of showing up. Passengers are not likely independent since people from the same family or company are likely to all show up or all not show. Even strangers arriving on an earlier incoming fight would not miss their fight independently if the fight was delayed. Passengers may all have roughly the same probability of showing up, but even this is suspect. People travelling in different fare categories or in different classes (e.g. charter fares versus first class) may have different probabilities of showing up.