Shapley Value

Game Theory
Knowledge Center

Albert Akos

Shapley Value

I have the following exercise and I am not sure about the calculation, if you could help me out, that would be awesome.
Consider the following characteristic function game: N = {1, 2, 3} and v({1}) = 0, v({2}) = 0, v({3}) = 0,
V({1,2}) = 40, v({1,3}) = 0, v({2,3}) = 50, v({1,2,3}) = 50. Find the core and the Shapley value.
Thanks in advance.

  Jaap de Jonge
Editor, Netherlands

What is Shapley Value?

The Shapley value is a solution model in cooperative game theory named after Lloyd Shapley, who first introduced and axiomatized it in 19531. It assigns a unique distribution among the participants of a total surplus generated by the coalition of all participants in any cooperative game. The Shapley value is characterized by a collection of desirable properties.

A cooperative setup is typically as follows: a coalition of participants cooperates, and obtains a certain overall gain (total benefits) from that cooperation. Because some participants may contribute more to the coalition than others, or some participants may possess different bargaining power, a particular final distribution of generated surplus among the players will arise in any particular game.
In other words it predicts, considering the importance of each participant to the overall cooperation, what payoff each participant can reasonably expect.

The formula is quite complex and can be found in Wikipedia.

Note that Shapley distributes the total gains to the players, assuming that they all collaborate, publicly share their contributions, and that a "fair" distribution has to be reached. As always, reality could be quite different from these assumptions...
1L.S. Shapley (1953). A value for n-person games. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games, volume II. Annals of Mathematics Studies 28. Princeton University Press, pp.307317.


More on Game Theory:
Game Theory vs. SWOT Analysis in the Strategy Process
Game Theory and Oligopolistic Competition
Types of Game Theory
🔥Gamification in Business and Management
What are the Uses of Game Theory? List of Usages
Can Game Theory deal with Bounded Rationality?
Using Game Theory for Making Investments
What is Dominance Theory?
👀Shapley Value
Best Practices
Game Theory in Business
Game Theory Cases in Strategy?
Is Business Strategy a Non-Zero-Sum Game?
Special Interest Group

Do you have a keen interest in Game Theory? Become our SIG Leader

Game Theory
Knowledge Center

About 12manage | Advertising | Link to us / Cite us | Privacy | Suggestions | Terms of Service
2022 12manage - The Executive Fast Track. V15.8 - Last updated: 5-7-2022. All names of their owners.