Definition
The Shapley Value is a concept in cooperative game theory used to measure a player’s contribution to the total payoff. Named after Lloyd Shapley, it determines the average marginal contribution of a player over all possible coalitions. It follows certain principles such as efficiency, symmetry, dummy player and additivity, ensuring a fair distribution among all players.
Key Takeaways
- Shapley Value is a solution concept in cooperative game theory. It is utilized to distribute a total payoff among players in a way that reflects their contribution to the total payoff.
- The Shapley Value is derived based on certain axioms such as efficiency, symmetry, dummy, and additivity. These collective properties are intended to provide a fair allocation reflecting each player’s value addition to the coalition.
- Shapley Value has varied applications in diverse fields, including economics, computer science, and finance. In finance, it is often used in cost and profit allocation, as well as in the valuation of derivative securities.
Importance
The Shapley Value is an important concept in finance because it provides a fair and equitable way to allocate rewards or costs within a cooperative game theory context.
Named after the Nobel Laureate Lloyd Shapley, it is a solution concept that ensures every participant receives a share proportional to their contribution.
By considering all possible orders of entry into a cooperation, it calculates the average expected marginal contribution of each participant.
This concept allows for a fair distribution, taking into account the different contributions of each player.
Thus, it’s especially useful in situations where payout needs to be decided among different contributors, like in joint ventures, cost and profit allocation, or cooperative marketing and pricing.
Explanation
The Shapley Value is a concept in game theory and economics that serves to determine the fair allocation of costs, profits, or other valuable elements among multiple participants in a cooperative context. It ensures every participant, or “player” in game theory parlance, receives a payout proportional to their contribution to the total output.
This principle is based on the value that each participant brings to the coalition, ensuring that the distribution of value is equitable and participants are neither overcompensated nor under-compensated. The Shapley Value is employed in a variety of practical applications.
For instance, it is used in business partnerships to calculate how much each partner deserves, or in supply chain collaborations to determine how the joint gains are distributed among the different partners involved. Consequently, it not only ensures fair profit or cost distribution, but also promotes collaboration and participation in cooperative environments, by ensuring all participants receive fair recognition for their contribution.
It can be a significant tool in deciding strategy and collaboration in both economics and business contexts.
Examples of Shapley Value
Ride-Sharing Apps: In example of the Shapley value in a real-world scenario is ride-sharing apps like Uber, Lyft, etc. These apps split the cost of a ride among multiple passengers who have shared the ride. The share of the cost per passenger can be calculated using the Shapley value, considering their respective starting and ending points, the number of passengers, and the total cost of the ride.
Electricity Markets: The Shapley Value can be used to fairly divide cost or benefits among participants in electricity markets. For instance, in a scenario where an electricity grid is shared by multiple energy producers, the Shapley value can help determine each producer’s contribution towards meeting the grid’s power demand and then allocate the earnings from the electricity sales proportionately.
Marketing Attribution: The Shapley value is applied to marketing attribution modelling to distribute the ‘credit’ for a sale to different marketing channels, considering all possible combinations of the channels and the sequential order they might be encountered by a buyer. This allows for fair allocation of revenue to each marketing channel, showing what each contributed to the final outcome. This concept is incredibly important for companies in their marketing strategy to understand which channels bring in the most revenue.
FAQs about Shapley Value
What is Shapley Value?
Shapley Value is a solution concept in cooperative game theory. Named after Lloyd Shapley, who introduced it in 1953, it is used to distribute the total payoff among the players of the game based on their individual contribution to the total payoff. It is widely used in fields like economics and computer science.
What are the properties of Shapley Value?
Shapley Value has four properties: Efficiency, Symmetry, Null player, and Additivity. Efficiency means the total payoff is distributed among all players. Symmetry means that players who contribute equally get the same payoff. Null player signifies that a player who does not contribute gets no payoff. Additivity means the value for two games combined equals the sum of the individual game values.
How is Shapley Value calculated?
Shapley Value is calculated based on the marginal contribution of a player, i.e., the additional value they bring when they join the game. The value is computed for all permutations and then averaged. The formula for the Shapley Value is a bit complex and is better explained through an example or graphical representation.
What are the applications of Shapley Value?
Shapley Value has diverse applications, particularly in fields that involve cooperative games or group interactions. This includes cost allocation, supply chain negotiations, voting power index, machine learning models, and more. It provides a theoretical framework to distribute rewards or costs fairly among the participants.
What is the significance of Shapley Value in finance?
In finance, Shapley Value can be used to determine the fair value of derivatives contracts or trading strategies. It can also be used to assess the contribution of different sectors or assets within a portfolio to its overall performance. This can help investors make informed decisions and allocate resources efficiently.
Related Entrepreneurship Terms
- Cooperative Game Theory
- Payoff Division
- Contributions of Players
- Coalitional Game
- Cost Allocation
Sources for More Information
- Investopedia: A comprehensive educational resource for all topics related to finance, including the Shapley Value.
- The Game Theory: A specialized website that has in-depth info about various principles of game theory, including the Shapley Value.
- Coursera: An online learning platform featuring courses on a wide variety of topics, including finance and potentially the Shapley Value.
- The Library of Economics and Liberty: This website offers resources for studying economics and features works from noted economists, potentially covering the Shapley Value.
