definition
staged
Payoff Vector
Given a coalitional game on player set $N$, a payoff vector is a function $$ x : N \to \mathbb{R}. $$ It specifies the final payoff allocated to each individual player.
The total payoff assigned to a coalition $S \subseteq N$ is $$ x(S) = \sum_{i \in S} x_i. $$ Coalitional-game solution concepts compare this allocated amount with the coalition worth $v(S)$.
Role In The Blueprint
This is the common input object for imputations ([[game_theory.cooperative_game.imputation]]), the core ([[game_theory.cooperative_game.core]]), and the Shapley value ([[game_theory.cooperative_game.shapley_value]]).
References
- [MSZ Ch.16, Def 16.1 and Def 16.13-16.16] Maschler, Solan, Zamir, Game Theory.