Bargaining Theory Introduction
Bargaining Theory is a part of Game Theory. It helps us understand how people make deals when:
- Each person wants what's best for themselves, but
- They must find a result that both sides can accept
The final deal depends on what each person wants, how long they can wait, and what happens if they can't agree.
The Nash Bargaining Solution
The Nash Bargaining Solution looks for a deal that:
- Gives both sides more than if they just walked away
- Balances things out when both people have the same "power"
The solution is found where the gains multiplied together reach the highest value.
We multiply gains because this gives the fairest balance: when both sides gain equally, the product is highest.
Example: Selling a Car
Sarah is selling her car.
- The car is worth $2,000 to Sarah (she won't sell for less)
- The car is worth $3,000 to Tom (he won't pay more)
There's an extra $1,000 of value between them! This is called the surplus.
- If Tom pays $2,500, both gain $500
- If Tom offers only $2,000, Sarah gains nothing extra
- If Sarah demands $3,000, Tom gains nothing extra
The table below shows the "extra" value each person gets:
| Final Sale Price | Sarah's Gain (Price − $2,000) |
Tom's Gain ($3,000 − Price) |
Nash Product (Sarah × Tom) |
|---|---|---|---|
| $2,000 | $0 | $1,000 | 0 |
| $2,250 | $250 | $750 | 187,500 |
| $2,500 (Fair Deal) | $500 | $500 | 250,000 (MAX) |
| $2,750 | $750 | $250 | 187,500 |
| $3,000 | $1,000 | $0 | 0 |
If they can't agree, they both get $0.
The Nash Bargaining Solution picks a split of (500, 500), where both sides gain equally.
Sharing the gains this way makes the deal strong and fair.
Working Together
Sometimes bargaining isn't just about splitting value, but about creating more of it first.
In Cooperative Bargaining, players find ways to grow the "total pie" before they cut it up.
A good cooperative deal has an important property:
- No one can do better without making the other person do worse
This means the deal is good because no value is wasted.
Example: A Business Partnership
Two companies are thinking about working together.
WizardEd makes great apps. They have good tech but few sales staff.
School Gear sells school supplies. They know many schools but don't know how to make apps.
- Alone, WizardEd earns $300,000
- Alone, School Gear earns $200,000
Staying apart they earn a total of $500,000.
But if they team up:
- WizardEd provides the software
- School Gear sells it through its existing school network
Together, they can reach more customers and earn $700,000.
By working together, they made $200,000 of extra value.
Any deal where both companies get more than before is a win.
They just need to decide how to split that extra $200,000!
Cooperation often leads to better outcomes, but it requires trust, communication, and clear rules.
When Bargaining Fails
Not every talk ends in a deal. Sometimes people won't budge, and the whole thing falls apart.
When this happens, both sides fall back to what they get without an agreement, often much less.
Example: The Strike
A company and its workers' union negotiate wages.
- If they agree, workers get paid and the company keeps operating
- If talks fail, workers strike and production stops
During a strike:
- The company loses money
- The workers lose pay
No one wins.
Even a "bad" deal can be better than no deal at all.
Flexibility matters.
Rigid strategies can turn a possible win–win situation into a guaranteed lose–lose outcome.
Summary
Bargaining Theory shows that people with different goals can still reach agreements that benefit everyone, and that:
- Fairness helps reach a deal
- Making more value is often better than fighting over what's there
- We can always walk away
By understanding people's goals we can turn conflict into opportunity.