
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
December 14th, 2012, 11:31 AM  #1 
Member Joined: Nov 2009 Posts: 90 Thanks: 0  How to Apply the Shapley Value Formula?
Trivia: This game theoretical formula is named after 2012 Nobel laureate Lloyd Shapley. The Shapley value is given by where is a coalition in the grand coalition and is the value generated by coalition . How do we apply this formula to a numerical example? Peter, Joe and Glenn are producing grunks and can choose to cooperate if they like. Their profit from producing grunks are . Using the formula for the Shapley value we can now obtain a 3tuple representing an allocation of profit such that . This is one of many potential solutions for this cooperative game. How can we apply the formula to find the solution? Apparently, it's something about imagining the players joining the game in different orders and thereby getting an average marginal value for each player. I don't see how to iterate in a numerical example. I understand that there are different orders in which all players can enter the grand coalition, but then I'm kinda lost. Any help is appreciated! 

Tags 
apply, formula, shapley 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
De Moivre's formula apply here?  WWRtelescoping  Complex Analysis  2  March 2nd, 2014 10:13 PM 
What is the correct way to apply quadratic formula?  king.oslo  Algebra  9  February 13th, 2013 06:02 AM 
Can I apply L'hopital here?  OriaG  Calculus  1  February 8th, 2013 01:24 AM 
Apply Simpson's rule: integration!  miner  Calculus  3  December 24th, 2011 09:17 PM 
Why does this apply to all tables except to a multiple of 3?  DragonsMath  Calculus  2  November 19th, 2010 07:34 AM 