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---++ Chapter 12: Teams of Selfish Agents: An Introduction to Coalitional Game Theory * *Page number: 388* * Section number: 12.2 * Date: 3/13/2010 * Name: Patrick Martin * Email: patrick(dot)martin(at)gatech(dot)edu * Content: I believe that Definition 12.2.1 should read x \in R^|N|, not x \in R^N. The same error is in Definition 12.2.2. * *Page number: 389* * Section number: 12.2.1 * Date: October 19, 2013 * Name: Marco Guazzone * Email: marco.guazzone@gmail.com * Content: In Theorem 12.2.7, I think that =$\phi(N,v)=\phi(N,v)$= should be replaced with =$\phi(N,v)=\varphi(N,v)$=. * *Page number: 392* * Section number:12.2.2 * Date:08/11/2012 * Name:Felix Fischer * Email:ff271(at)cam * Content: Bondereva should be Bondareva, also on the following page * *Page number: 393* * Section number:12.2.2 * Date:08/11/2012 * Name:Felix Fischer * Email:ff271(at)cam * Content: In the proof of Theorem 12.2.11, the sum in the first constraint of the dual is missing the condition i\in S. * *Page number: 396* * Section number:12.2.3 * Date:30/10/2012 * Name:Felix Fischer * Email:ff271(at)cam * Content: In Definition 12.2.18, ``the optimal solution to O_{i−1}'' is ambiguous. There can be more than one optimal solution, and to obtain the nucleolus one in fact has to fix only those constraints that are tight in _every_ optimal solution. Consider the game where v({1})=4, v({2})=3, v({3})=2, v({1,2})=10, v({1,3})=11, v({2,3})=5, v({1,2,3})=12. Both (8,2,2) and (15/2,2,5/2) are optimal solutions of O_1 for this game, only the latter is in the nucleolus. Fixing the constraint for {2,3}, which is tight for the former solution, does not lead to the nucleolus. ---+++ The following errors are fixed in the second printing of the book and online PDF v1.1 * *Page number: 389* * Section number: 2 * Date: October 22, 2008 * Name: Mike Rogers * Email: mikepr@cs.stanford.edu * Content: The formula for the Shapley value has N! where it should have |N|! -- Main.KevinLeytonBrown - 13 Nov 2008
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