Chapter 6: Richer Representations: Beyond the Normal and Extensive Forms

• Page number: 162
• Section number: 6.2.3
• Date:11/18/11
• Name:Eugene Vorobeychik
• Email:eug.vorobey@gmail.com
• Content:"there exists an linear programming formulation" => a linear programming formulation
• Page number: 162
• Section number:6.2.3
• Date:11/18/11
• Name:Eugene Vorobeychik
• Email:eug.vorobey@gmail.com
• Content:The first paragraph implies that general-sum single-controller stochastic games can be solved in polynomial time. A special case of such games are general-sum finite-action games, for which no poly-time procedure exists. I believe what is meant are zero-sum single-controller games (I believe Filar and Vrieze (1997) offer a linear programming formulation for this case).
• Page number: 174
• Section number:6.4.1
• Date:04/19/2014
• Content:Definition 6.4.1. "R is a set of r resources" -> "R is a set of k resources". This is a minor point, but throughout sections 6.4.1-6.4.4, "r" is being used for referring to a certain resource in R. Also in comparison, Definition 6.4.7 (for nonatomic version) states "R is a set of k resources".
Similarly, "c = (c_1, \dots, c_r) where c_k ... is a cost function for resource k \in R" should be changed to "c = (c_1, \dots, c_k) where c_r is a cost function for resource r \in R" (also see Definition 6.4.7 for comparison).
• Page number: 175
• Section number:6.4.2
• Date:04/04/2014
• Content:"However, if we run MyopicBestResponse with a = (L, U) ..." => (U, L) just to be consistent with the convention of this book that specifies the row player's action first.
• Page number: 177
• Section number:6.4.3
• Date:04/19/2014
• Content: Proof of Theorem 6.4.6 (Every congestion game is a potential game.).
In the equations of the proof, "c_r(j + 1)" should be changed to "c_r(#(r, a_{-i}) + 1)" (this occurs twice). Notice that j appears in the summation and runs from 1 to #(r, (a_{-i})).
• Page number: 177
• Section number:6.4.3
• Date:04/19/2014
• Content: In the proof of Theorem 6.4.6, the potential function is defined to be "P(a) = \sum_{r\in R} ..." but it should be negated, i.e. "P(a) = - \sum_{r\in R} ..." because the book earlier defined the utility function to be a negated sum of costs (see the paragraph after Definition 6.4.1). Otherwise, the proof would actually show that "P(a_i, a_{-i}) - P(a'_i, a_{-i}) = ... = - u_i(a_i, a_{-i}) + u_i(a'_i, a_{-i})" (which is not what we want).

The following errors are fixed in the second printing of the book and online PDF v1.1

• Page number:
• Section number:6.4.3
• Date:7/3/09
• Name:Kevin Leyton-Brown
• Content:In the proof of Theorem 6.4.3, "because by construction $u_i(a'_i,a_{-i}) > u_(a_i,a_{-i})$" should read "because by construction $u_i(a'_i,a_{-i}) > u_i(a_i,a_{-i})$". (That is, there's a missing subscripted i after the u following the > sign. The left bracket shouldn't be subscripted.)
• Page number: 163 (print version)
• Section number:
• Page (print version): more conceptually complicated => conceptually more complicated
• Date: April 27 2009
• Name:Yoav
• Email:
• Content:
تسريع الانترنت

-- KevinLeytonBrown - 13 Nov 2008

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