The Shapley value is a concept from game theory that measures the fairness of a particular allocation of resources. It was first proposed by Lloyd Shapley in 1953.

The idea is to consider all possible ways in which the resources could be allocated, and then to calculate the average value of each allocation. The allocation that gives each person the highest average value is the fair allocation.

The Shapley value has a number of applications in economics, including the allocation of goods and services in an economy, the design of fair voting systems, and the division of profits among shareholders.

##### What does Shap do in Python?

Shap is a python library that allows for the computation of Shapley values in games. Shapley values are a way of measuring the contribution of each player to the overall game. They are named after Lloyd Shapley, who first proposed them in 1953.

The idea behind Shapley values is that they represent the mean contribution of a player over all possible coalitions. To compute the Shapley value of a player, we first need to enumerate all of the possible coalitions that could be formed. For each coalition, we then need to compute the player's contribution to that coalition. Finally, we take the mean of all of the player's contributions.

Shapley values have a number of nice properties, which make them a useful tool for measuring player contributions. First, they are symmetric, meaning that the Shapley value of a player does not depend on the order in which the players are listed. Second, they are efficient, meaning that the Shapley value of a player is the same as their actual contribution to the game. Third, they are null if the player makes no contribution to the game.

One of the advantages of Shapley values is that they can be computed in polynomial time. This makes them particularly well-suited for large games, where other methods of measuring player contributions (such as the Nash bargaining solution) become infeasible. What is Shap base value? The Shap base value is the average value of the function that the model is trying to predict. For example, if the model is trying to predict the price of a house, the Shap base value would be the average price of a house. This value is used to help explain the model's predictions. What is a dummy player game theory? Dummy player game theory is the study of how rational players can best take advantage of an opponent who is not playing rationally. This can be done by finding patterns in the opponent's behavior, and then using these patterns to predict what the opponent will do next. This can be used to exploit the opponent's weaknesses, and to ultimately win the game. What is the core of a coalitional game? A coalitional game is a game in which players form coalitions in order to gain a cooperative advantage. The core of a coalitional game is the set of Nash equilibria in which no coalition has an incentive to deviate from its current coalition. Is Shapley value in the core? The Shapley value is not in the core. The core is the set of feasible allocations that are Pareto efficient and maximally fair. The Shapley value is a fair allocation, but it is not Pareto efficient.