The Shapley Value is a concept in cooperative game theory that assigns a value to each player in a coalition game. It represents the average contribution of a player to all possible coalitions in which they participate. This calculator simplifies the process of determining Shapley Values for different players within a cooperative game.
Formula: The Shapley Value for a player in a coalition game is calculated based on their marginal contributions to all possible coalitions. The formula is complex and involves considering all permutations of players in coalitions. The Shapley Value for a player ‘i’ is given by the sum over all possible permutations of the game’s characteristic function.
How to Use:
- Enter the values for each coalition separated by commas in the provided input field.
- Click the “Calculate Shapley Value” button to initiate the calculation.
- The result will be displayed below the button, showing the Shapley Value for the specified coalition values.
Example: Suppose we have a coalition game with three players, and the values for different coalitions are 10, 15, and 20. Enter these values into the input field, click “Calculate Shapley Value,” and the result will provide the Shapley Value for each player.
FAQs:
- Q: What is the Shapley Value? A: The Shapley Value is a concept in cooperative game theory that assigns a value to each player based on their marginal contributions to different coalitions.
- Q: How is the Shapley Value calculated? A: The calculation involves considering all possible permutations of players in coalitions, making it a complex formula.
- Q: Can this calculator handle any number of players? A: Yes, the calculator is designed to handle different numbers of players within a coalition game.
Conclusion: The Shapley Value Calculator simplifies the determination of Shapley Values for cooperative games. Understanding the contributions of each player is crucial for fair distribution of gains in collaborative scenarios. Use this calculator to explore and analyze Shapley Values efficiently in various cooperative game settings.