ShapleyShubikindeksiä

ShapleyShubikindeksiä is a concept used in cooperative game theory to measure the power or influence of a player within a coalition. It is derived from the Shapley value, which assigns a unique distribution of a total surplus generated by a coalition of players. The ShapleyShubikindeksiä specifically focuses on the proportion of the total value that a player can expect to obtain.

The index is calculated by considering all possible orderings in which players can join a coalition. For each ordering, the marginal contribution of a player to the coalition formed by those who joined before them is determined. The ShapleyShubikindeksiä for a player is the average of these marginal contributions across all possible orderings. This averaging process ensures that each player's influence is assessed fairly, taking into account their potential contributions at various stages of coalition formation.

A higher ShapleyShubikindeksiä indicates that a player has more power or a greater ability to influence the outcome of the coalition. Conversely, a lower index suggests less influence. The sum of the ShapleyShubikindeksiä for all players in a game will always equal one, representing the total value generated by the grand coalition. This index is useful in various applications, including political science, economics, and resource allocation, to understand how decision-making power is distributed among participants.