Method and system for using cooperative game theory to resolve statistical joint effects

A method for constructing an access relationship between coalitions in a statistical cooperative game and a multivariate statistical model, comprising:

• identifying a plurality of elements of the multivariate statistical model;
• identifying a set of coalitions in the statistical cooperative game;
• and
• specifying an access relationship comprising a set of rules, wherein the set of rules determine for selected coalitions in the identified set of coalitions, elements that are accessible by the coalition and how the accessible elements may be used by the coalition.

A method for determining a worth for selected coalitions in a statistical cooperative game, comprising:

• selecting a performance measure of a multivariate statistical model;
• computing a performance measure for selected collations in the statistical cooperative game based on elements of the multivariate statistical model accessible by a selected coalition;
• and
• determining, for each coalition from the selected set of coalitions, a worth of a coalition in the statistical cooperative game based on the computed performance measure for that coalition.

A method for allocating a worth of a coalition in a cooperative game on a multiplicative basis, comprising:

• generating a second cooperative game from a first cooperative game by setting a worth of a plurality of coalitions in the second cooperative game to a logarithm of the worth of a same coalition plus a constant;
• applying a cooperative allocation procedure to the second cooperative game;
• and
• creating an allocation for a player in the first cooperative game from an allocation in the second cooperative game by applying an antilog to a value allocated to a player in the statistical cooperative game and subtracting a constant.

A method to estimate a total effect of a basic variable on an individual observation, set of observations, or forecast value in a multivariate statistical model with interaction variables, comprising:

• constructing a multivariate statistical model with basic variables and a plurality of interaction variables derived from the basic variables;
• identifying an access relationship between coalitions in a statistical cooperative game and elements of the multivariate statistical model, including the basic and interaction independent variables;
• constructing a cooperative game based on the access relationship;
• and
• applying a value function or other allocation rule to the cooperative game to attribute all effects among players in the game.

A cooperative game resolution system, comprising in combination:

• a plurality of software modules stored as data bits in memory on one or more computers with one or more processors, the plurality of software modules including:
• a player module for identifying a set of players for a statistical cooperative game,
• an access module for identifying an access relationship between coalitions of the statistical cooperative game and elements of a multivariate statistical, wherein a selected subset of the identified players is a coalition, and
• a worth module for determining a worth for selected coalitions in the statistical cooperative game based on elements of the multivariate statistical model accessible by a coalition or for determining a worth of a coalition in a cooperative game on a multiplicative basis;
• and
• one or more databases for storing cooperative game data.