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Interactive module

Shapley Value

Average each teammate’s marginal contribution across every joining order.

Rule ledger

caseThree teammates produce a $1000 project, but their value depends on who collaborates.
rulephi_i = sum_S |S|!(n-|S|-1)!/n! * [v(S union {i}) - v(S)]
questionWhen one strategy changes alone, whose payoff or fairness changes first?

Project Credit Split

joins #1

Ava

coalition value $260

joins #2

Ben

coalition value $620

joins #3

Chloe

coalition value $1,000

1

Ava -> Ben -> Chloe

2

Ava -> Chloe -> Ben

3

Ben -> Ava -> Chloe

4

Ben -> Chloe -> Ava

5

Chloe -> Ava -> Ben

6

Chloe -> Ben -> Ava

Ava fair payment

$390

Ben fair payment

$330

Chloe fair payment

$280

How to read this result

The Shapley value checks every joining order and averages the extra value each person adds. That avoids giving credit only by looking at the final team.

Formula

phi_i = sum_S |S|!(n-|S|-1)!/n! * [v(S union {i}) - v(S)]

Fair payment is the average value a person adds when arriving to every possible team.

Step-by-step Explanation

Scenario

Three teammates produce a $1000 project, but their value depends on who collaborates.

Why This Matters

The Shapley value is used for bonuses, cost sharing, attribution, and cooperative AI analysis.

Beginner-Friendly Summary

Instead of arguing about credit, measure how much each person changes the value of every coalition.

Try changing the strategy and watch which result changes first.