What is a characteristic function in game theory?
Definition 1 By a characteristic function of an n-person game we mean a function v that assigns a value to each subset of players; i.e v : 2N ↦→ R.
What are cooperative and non cooperative games?
Definition: Cooperative game theory focuses on how much players can appropriate given the value each coalition of player can create, while non-cooperative game theory focuses on which moves players should rationally make.
What are cooperative games in game theory?
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players (“coalitions”) due to the possibility of external enforcement of cooperative behavior (e.g. through contract law).
How is Shapley value calculated?
The Shapley value is computed by taking the average of difference from all combinations. Essentially, the Shapley value is the average marginal contribution of a feature considering all possible combinations.
How a characteristic function form is used to analyze games?
The characteristic-function form is generally used to analyze games with more than two players. It indicates the minimum value that each coalition of players—including single-player coalitions—can guarantee for itself when playing against a coalition made up of all the other players.
What is a payoff vector?
Since the payoffs to each player are different, we will use ordered pairs where the first number is Player 1’s payoff and the second number is Player 2’s payoff. The ordered pair is called the payoff vector.
What is the cooperative outcome?
What is the cooperative outcome? The cooperative outcome would maximize joint payoffs. This would occur if Firm 1 goes for the low end of the market and Firm 2 goes for the high end of the market. The joint payoff is 1,500 (Firm 1 gets 900 and Firm 2 gets 600).
What is lime and Shap?
On the other hand, I use SHAP mostly for summary plots and dependence plots. Maybe using both will help you to squeeze out some additional information. But in general: Use LIME for single prediction explanation. Use SHAP for entire model (or single variable) explanation.
What is Shapley value explain?
The Shapley value is the average of all the marginal contributions to all possible coalitions. The computation time increases exponentially with the number of features. One solution to keep the computation time manageable is to compute contributions for only a few samples of the possible coalitions.