Shapley Value, explained.
The Shapley value allocates a cooperative game's total value by averaging each participant's marginal contribution over all joining orders.
Why it happens
Singletons create zero; AB creates 60, AC 20, BC 40 and ABC 90. Inspect six permutations, calculate the added value when each participant joins, then average the contributions. The resulting allocation is A=30, B=40, C=20.
The Shapley value allocates a cooperative game's total value by averaging each participant's marginal contribution over all joining orders.
Read the result
A participant's contribution in one order need not match the average. Check that all assigned contributions sum to the grand coalition's value.
A worked example
Three collaborators create ninety units
Inspect A→B→C: A adds zero, B adds sixty and C adds thirty as the coalition grows.
Switch to B→C→A: B adds zero, C adds forty and A adds fifty, despite unchanged coalition values.
Average all six orders to obtain A thirty, B forty and C twenty. The allocation depends on the specified coalition-value table.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Singletons create zero; AB creates 60, AC 20, BC 40 and ABC 90. Inspect six permutations, calculate the added value when each participant joins, then average the contributions. The resulting allocation is A=30, B=40, C=20.
Where this idea is useful
A practical use
A collaboration can distinguish contribution to a coalition from a simple count of hours or the value a member creates alone.
A common misconception
“Standalone value alone determines a fair share.”
A participant can create little alone and add substantial value in combination. The Shapley rule formalises one allocation principle rather than establishing universal desert.
What this explanation leaves out
- The coalition values are authored and transferable utility is assumed. The Shapley value is a solution concept under specified axioms, not an empirical measure of worth or a universally accepted account of fairness.
Can I use these shares to divide a real team's salary?
Only after justifying a transferable-value model and its coalition estimates. Actual compensation also involves rights, contracts and fairness considerations absent from this teaching table.
What evidence would support the coalition values before debating how the surplus should be divided?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.