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An Analysis of the Shapley Value and its Uncertainty for the Voting Game

An Analysis of the Shapley Value and its Uncertainty for the Voting Game
An Analysis of the Shapley Value and its Uncertainty for the Voting Game
The Shapley value provides a unique solution to coalition games and is used to evaluate a player’s prospects of playing a game. Although it provides a unique solution, there is an element of uncertainty associated with this value. This uncertainty in the solution of a game provides an additional dimension for evaluating a player’s prospects of playing the game. Thus, players want to know not only their Shapley value for a game, but also the associated uncertainty. Given this, our objective is to determine the Shapley value and its uncertainty and study the relationship between them for the voting game. But since the problem of determining the Shapley value for this game is #P-complete, we first present a new polynomial time randomized method for determining the approximate Shapley value. Using this method, we compute the Shapley value and correlate it with its uncertainty so as to allow agents to compare games on the basis of both their Shapley values and the associated uncertainties. Our study shows that, a player’s uncertainty first increases with its Shapley value and then decreases. This implies that the uncertainty is at its minimum when the value is at its maximum, and that agents do not always have to compromise value in order to reduce uncertainty.
39-52
Fatima, S.
63e6d4ad-830e-4b14-baf4-90d7d34eca30
Wooldridge, M.
955b6c39-0d07-430e-b68d-b9a96d6e14e7
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Fatima, S.
63e6d4ad-830e-4b14-baf4-90d7d34eca30
Wooldridge, M.
955b6c39-0d07-430e-b68d-b9a96d6e14e7
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Fatima, S., Wooldridge, M. and Jennings, N. R. (2005) An Analysis of the Shapley Value and its Uncertainty for the Voting Game. 7th International Workshop on Agent-Mediated Electronic Commerce, Netherlands. pp. 39-52 .

Record type: Conference or Workshop Item (Paper)

Abstract

The Shapley value provides a unique solution to coalition games and is used to evaluate a player’s prospects of playing a game. Although it provides a unique solution, there is an element of uncertainty associated with this value. This uncertainty in the solution of a game provides an additional dimension for evaluating a player’s prospects of playing the game. Thus, players want to know not only their Shapley value for a game, but also the associated uncertainty. Given this, our objective is to determine the Shapley value and its uncertainty and study the relationship between them for the voting game. But since the problem of determining the Shapley value for this game is #P-complete, we first present a new polynomial time randomized method for determining the approximate Shapley value. Using this method, we compute the Shapley value and correlate it with its uncertainty so as to allow agents to compare games on the basis of both their Shapley values and the associated uncertainties. Our study shows that, a player’s uncertainty first increases with its Shapley value and then decreases. This implies that the uncertainty is at its minimum when the value is at its maximum, and that agents do not always have to compromise value in order to reduce uncertainty.

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Published date: 2005
Venue - Dates: 7th International Workshop on Agent-Mediated Electronic Commerce, Netherlands, 2005-01-01
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 261134
URI: http://eprints.soton.ac.uk/id/eprint/261134
PURE UUID: df919e28-4309-40e5-812d-b5581e5dddb8

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Date deposited: 10 Aug 2005
Last modified: 19 Jul 2019 22:35

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