About Cooperative Resolution

The proportional value has an important property relevant to statistical theory. A player that can achieve nothing alone, call him a zero player, must receive zero value. Relate a cooperative game to a statistical model by associating each factor with a different player in the game. Define the worth of a coalition as the marginal contribution to explained variance of the factors controlled by the players in the coalition. 

The game just defined is a statistical cooperative game. The worth of a single player in this type of game is the marginal contribution to explained variance of his factor. The proportional value of the resulting game will assign a zero variance share to a player that controls a factor with zero marginal contribution to explained variance.

The fact that zero players must receive zero value is a clue that the proportional value of a statistical cooperative game may be of interest in statistical analysis. Contrary-wise, a value that assigns a positive variance share to a zero player should be considered suspect from the vantage of statistical theory. This is the case with the Shapley value of a statistical cooperative game.

Cooperative resolution refers to constructing an association between a cooperative game and a statistical model, and then using a cooperative solution concept such as the Shapley or proportional values to perform the decomposition.

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