◄ WORLD V · SONNY 5DART 573 · a helldive across the board

THE SHAPLEY VALUE your fair share of what the team made

When a coalition produces value together, how much did each member contribute? The Shapley value is the unique answer satisfying fairness: average each player’s marginal contribution over every possible order of joining. It is the only rule that is efficient (shares the whole), symmetric (equals for equals), gives nothing to null players, and adds across games. Shapley won the 2012 Nobel; the value now explains machine-learning predictions.

THE TECHNIQUE φₖ = average marginal contribution

The demo computes a symmetric 3-player game’s Shapley values over all 6 orderings and checks efficiency: live demo







  
HISTORY & CREDIT Shapley · 1953

  
“The Shapley value is one of several fair rules.” — it is the unique value satisfying efficiency, symmetry, the null-player axiom, and additivity together. cited

  
marginal · how much a player adds when they join a coalition.
average · over all orderings of arrivals — the only fair, efficient, symmetric split.
1953 · Lloyd Shapley (Nobel 2012); today it grounds SHAP feature attribution in ML.

  
Credit, averaged over every way the team could form. theorem






  
RECOMMEND FOR I-13 efficiency, on the compiler

  
On i-13, a symmetric game (v=1 iff |S|≥2) gives φ₁=1/3, and the three shares sum to v(N)=1:

  
$ i13 run gm_shapley-value.i13
RUN OK · 151 step(s)
phi1 = 0.3333...   -- 2/6, averaged over 6 orderings
efficiency = 1     -- 3 * phi = v(N)
sums_to_vN = 1

  
Recommend as a NULL — a uniqueness theorem (B39). The Shapley value is the unique map pinned by its four axioms; every correct computation returns the same shares. NULL — your fair share of what the team made.