## 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@gmailDELETEthisTEXT.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@csDELETEthisTEXT.stanford.edu
• Content: The formula for the Shapley value has N! where it should have |N|!
-- KevinLeytonBrown - 13 Nov 2008
Topic revision: r7 - 2013-10-19 - MarcoGuazzone

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