Definition Marginal Contribution

definition staged

#

Lean declarations

def CoalitionalGame.marginalContrib EconCSLib @ cef01c7, EconCSLib.GameTheory.CoalitionalGame.ShapleyValue
The marginal contribution of player `i` to coalition `S` (where `i ∉ S`).
```
def marginalContrib (i : N) (S : Finset N) : ℝ :=
  G.v (insert i S) - G.v S
```

Modules: EconCSLib.GameTheory.CoalitionalGame.ShapleyValue

Marginal Contribution

The marginal contribution of player $i$ to a coalition $S$ not containing $i$ is $$ v(S \cup \{i\}) - v(S). $$

This is the payoff increment created by adding $i$ to $S$. Shapley-value formulae average this quantity over all possible predecessor coalitions.

References

[MSZ Ch.18, §18.2] Maschler, Solan, Zamir, Game Theory.

Used by

Shapley Value

Also in