Game Theory Questions Medium
Coalitional game theory is a branch of game theory that focuses on analyzing and predicting the behavior of groups or coalitions of players in a game. In coalitional games, players can form alliances or coalitions with other players to achieve their objectives. The concept of coalitional game theory revolves around studying how these coalitions are formed, how they interact, and how they distribute the benefits or payoffs among their members.
In coalitional game theory, the characteristic function is a key concept. It assigns a value to each possible coalition, representing the worth or utility that the coalition can achieve. This value is typically based on the outcomes or payoffs that the coalition can obtain by working together.
The Shapley value is a widely used solution concept in coalitional game theory. It provides a way to fairly distribute the total value generated by a coalition among its members. The Shapley value considers all possible orderings of players joining the coalition and calculates the average marginal contribution of each player to the coalition's worth.
Another important concept in coalitional game theory is the core. The core represents a set of payoff allocations that are stable and cannot be improved upon by any subgroup of players. It ensures that no coalition has an incentive to deviate from the current allocation.
Overall, coalitional game theory provides insights into how groups of players can strategically form alliances and negotiate to achieve their objectives in a cooperative setting. It has applications in various fields, including economics, political science, and computer science.