Difference: RicherRepresentationsErrata (1 vs. 8)

Revision 82020-03-13 - MichaelSanderson

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

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تسريع الانترنت
 -- KevinLeytonBrown - 13 Nov 2008

Revision 72017-04-23 - EditaStewart

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

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تسريع الانترنت
 -- KevinLeytonBrown - 13 Nov 2008

Revision 62014-04-20 - HadenLee

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

  • Page number: 162
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    • 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).
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  • Page number: 174
    • Section number:6.4.1
    • Date:04/19/2014
    • Name:Haden Hooyeon Lee
    • Email:haden[dot]lee[at]stanford[dot]edu
    • 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
    • Name:Haden Hooyeon Lee
    • Email:haden[dot]lee[at]stanford[dot]edu
    • 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.
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  • Page number: 177
    • Section number:6.4.3
    • Date:04/19/2014
    • Name:Haden Hooyeon Lee
    • Email:haden[dot]lee[at]stanford[dot]edu
    • 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
    • Name:Haden Hooyeon Lee
    • Email:haden[dot]lee[at]stanford[dot]edu
    • 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

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    • Section number:6.4.3

Revision 52014-04-04 - HadenLee

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META TOPICPARENT name="Errata"

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

  • Page number: 162
Line: 13 to 13
 
    • 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).
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  • Page number: 175
    • Section number:6.4.2
    • Date:04/04/2014
    • Name:Haden Hooyeon Lee
    • Email:haden[dot]lee[at]stanford[dot]edu
    • 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.
 

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

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    • Section number:6.4.3

Revision 42011-11-18 - YevgeniyVorobeychik

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  • 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).
 

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

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Revision 32010-02-23 - KevinLeytonBrown

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

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    • 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.)
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    • Page (print version): more conceptually complicated => conceptually more complicated
    • Date: April 27 2009
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Revision 22009-07-04 - KevinLeytonBrown

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    • 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.)
 
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-- KevinLeytonBrown - 13 Nov 2008

 
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