# Difference: ComputingNormalFormErrata (1 vs. 15)

#### Revision 152020-05-28 - LeiZhou

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

>
>
• Page number: 100 (electronic version, Revision 1.1)
• Section number: 4.2.2
• Date: May 28, 2020
• Name: Lei Zhou
• Email: leizhou[at]pku[dot]edu[dot]cn
• Content: In "Each such equation has the form v=c+qu+T, where v is the clashing variable, c is a constant (initially they are all 1), u is the entering variable, q is a constant coefficient, and T is a linear combination of variables other than v or u. The clashing variable to leave is the one in whose equation the q/c ratio is smallest", the ratio should be c/|q| (used in the examples followed). In "At this point the algorithm terminates since, between them, Equations (4.25) and (4.24) contain all the labels”, I think the algorithm terminates because all the labels are contained in the basis. In "Renormalizing the vectors x′ and y′ to be proper probabilities, one gets the solution ((2/3,1/3, 0), (1/3,2/3)) ...", the solution is got by first setting all the variables in the right-hand side of Equations (4.25) and (4.24) to be zero and then renormalizing the vectors x' and y'.

• Page number: 95 (first edition)
• Section number: 4.2.2

#### Revision 142020-05-05 - BrianLunday

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

• Page number: 95 (first edition)
• Section number: 4.2.2
• Date: May 2, 2020
Changed:
<
<
• Name: Brian L.
>
>
• Name: Brian Lunday
• Email: brian[dot]lunday[at]afit[dot]edu

• Content: In Figure 4.4, the label (2/3, 1/3, 0) on graph G_1 should be reordered to read (0, 2/3, 1/3) to correspond with the entries (a_1^3, a_2^2, a_2^2)

• Page number: 97 (first edition)

#### Revision 132020-05-03 - BrianLunday

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Changed:
<
<
• Page number: 97 (first edition)
>
>
• Page number: 95 (first edition)
• Section number: 4.2.2
• Date: May 2, 2020
• Name: Brian L.
• Content: In Figure 4.4, the label (2/3, 1/3, 0) on graph G_1 should be reordered to read (0, 2/3, 1/3) to correspond with the entries (a_1^3, a_2^2, a_2^2)

• Page number: 97 (first edition)

• Section number: 4.2.2
• Date: January 6 2014
• Name: Danny

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Line: 7 to 7

• Date: January 6 2014
• Name: Danny
• Content: In "... the one in whose equation the q/c ratio is smallest", the ratio should be c/q (at least that is what is used in the example that follows in the text).
>
>
• Page number: 114 (electronic version)
• Section number: 4.6 (Theorem 4.6.1)
• Date: March/10/2015
• Content: The theorem states that "The following problems are [...] guaranteed payoff, subset inclusion, and subset containment." However, I don't think that "subset inclusion" and "subset containment" were mentioned in the section previously. Comparing this to Theorem 4.2.3, I wonder if these were meant to be "action inclusion" and "action exclusion" instead.

• Page number:
• Section number:
• Date:
Line: 26 to 32

• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2
Deleted:
<
<
-- KevinLeytonBrown - 13 Nov 2008
\ No newline at end of file
>
>
-- KevinLeytonBrown - 13 Nov 2008

#### Revision 112014-01-07 - DannyD

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Changed:
<
<
• Page number:
• Section number:
• Date:
• Name:
• Email:
• Content:
>
>
• Page number: 97 (first edition)
• Section number: 4.2.2
• Date: January 6 2014
• Name: Danny
• Content: In "... the one in whose equation the q/c ratio is smallest", the ratio should be c/q (at least that is what is used in the example that follows in the text).

• Page number:
• Section number:
• Date:
Line: 27 to 26

• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2
Deleted:
<
<

-- KevinLeytonBrown - 13 Nov 2008
\ No newline at end of file
>
>
-- KevinLeytonBrown - 13 Nov 2008
\ No newline at end of file

#### Revision 102010-03-04 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Deleted:
<
<
• Page number: 99 (electronic version)
• Section number: 4.2.2
• Date: June 23 2009
• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2

• Page number:
• Section number:
• Date:
Line: 27 to 21

• Name:Kevin
• Section: 4.2.1
• Content:After "We can now state the main complexity result.", add a footnote: "This theorem describes the problem of approximating a Nash equilibrium to an arbitrary, specified degree of precision (i.e., computing an $\epsilon$-equilibrium for a given $\epsilon$). The equilibrium computation problem is defined in this way partly because games with three or more players can have equilibria involving irrational-valued probabilites."
>
>
• Page number: 99 (electronic version)
• Section number: 4.2.2
• Date: June 23 2009
• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2

-- KevinLeytonBrown - 13 Nov 2008 \ No newline at end of file

#### Revision 92010-03-02 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Line: 27 to 27

• Name:Kevin
• Section: 4.2.1
• Content:After "We can now state the main complexity result.", add a footnote: "This theorem describes the problem of approximating a Nash equilibrium to an arbitrary, specified degree of precision (i.e., computing an $\epsilon$-equilibrium for a given $\epsilon$). The equilibrium computation problem is defined in this way partly because games with three or more players can have equilibria involving irrational-valued probabilites."
Deleted:
<
<
• Page number: 96-7 (print version)
• Section number:4.2.2
• Page (print version):
• Date: April 27 2009
• Name:Yoav
• Email:
• Content:The tabbings are wrong in the running example of the pivoting alg

-- KevinLeytonBrown - 13 Nov 2008 \ No newline at end of file

#### Revision 82010-02-23 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

>
>
• Page number: 99 (electronic version)
• Section number: 4.2.2
• Date: June 23 2009
• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2
• Page number:
• Section number:
• Date:
• Name:
• Email:
• Content:
• Page number:
• Section number:
• Date:
• Name:
• Email:
• Content:

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

• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
Line: 14 to 34

• Name:Yoav
• Email:
• Content:The tabbings are wrong in the running example of the pivoting alg
Deleted:
<
<
• Page number: 163 (print version)
• Section number:
• Page (print version): more conceptually complicated => conceptually more complicated
• Date: April 27 2009
• Name:Yoav
• Email:
• Content:
• Page number: 99 (electronic version)
• Section number: 4.2.2
• Date: June 23 2009
• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2

-- KevinLeytonBrown - 13 Nov 2008

#### Revision 72009-06-23 - NicolasDudebout

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Line: 21 to 21

• Name:Yoav
• Email:
• Content:
Deleted:
<
<
-- KevinLeytonBrown - 13 Nov 2008
\ No newline at end of file
>
>
• Page number: 99 (electronic version)
• Section number: 4.2.2
• Date: June 23 2009
• Name: Nicolas Dudebout
• Email:
• Content: Equation (4.25) r3 = 1/4 - 3/4 r1 - 3/2 r2 should be r3 = 1/4 - 3/4 r1 + 3/2 r2

-- KevinLeytonBrown - 13 Nov 2008

#### Revision 62009-05-31 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

>
>
• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
• Section: 4.2.1
• Content:After "We can now state the main complexity result.", add a footnote: "This theorem describes the problem of approximating a Nash equilibrium to an arbitrary, specified degree of precision (i.e., computing an $\epsilon$-equilibrium for a given $\epsilon$). The equilibrium computation problem is defined in this way partly because games with three or more players can have equilibria involving irrational-valued probabilites."

• Page number: 96-7 (print version)
• Section number:4.2.2
• Page (print version):
Line: 15 to 21

• Name:Yoav
• Email:
• Content:
Deleted:
<
<
• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
• Section: 4.2.1
• Content:After "We can now state the main complexity result.", add a footnote: "This theorem describes the problem of computing a Nash equilibrium to an arbitrary, specified degree of precision (i.e., computing an $\epsilon$-equilibrium for a given $\epsilon$), rather than exactly. This definition of the equilibrium computation problem is justified partly by the fact that there exist games with three or more players in which equilibrium strategies involve irrational-valued probabilites."
-- KevinLeytonBrown - 13 Nov 2008 \ No newline at end of file

#### Revision 52009-05-30 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

• Page number: 96-7 (print version)
Line: 19 to 19

• Date: May 28 2009
• Name:Kevin
• Section: 4.2.1
Changed:
<
<
• Content:After "We can now state the main complexity result.", add: "This theorem describes the problem of computing a Nash equilibrium to an arbitrary, specified degree of precision, rather than computing it exactly. This is partly because some games with three or more players have only equilibria whose mixed strategies involve irrational numbers."
>
>
• Content:After "We can now state the main complexity result.", add a footnote: "This theorem describes the problem of computing a Nash equilibrium to an arbitrary, specified degree of precision (i.e., computing an $\epsilon$-equilibrium for a given $\epsilon$), rather than exactly. This definition of the equilibrium computation problem is justified partly by the fact that there exist games with three or more players in which equilibrium strategies involve irrational-valued probabilites."
-- KevinLeytonBrown - 13 Nov 2008

#### Revision 42009-05-29 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

• Page number: 96-7 (print version)
Line: 18 to 18

• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
Changed:
<
<
• Email:
• Content:In Theorem 4.2.1, the text "or more players" should be dropped--finding a sample Nash equilibrium in a 3+ player game is PPAD-hard, not PPAD-complete.
>
>
• Section: 4.2.1
• Content:After "We can now state the main complexity result.", add: "This theorem describes the problem of computing a Nash equilibrium to an arbitrary, specified degree of precision, rather than computing it exactly. This is partly because some games with three or more players have only equilibria whose mixed strategies involve irrational numbers."
-- KevinLeytonBrown - 13 Nov 2008 \ No newline at end of file

#### Revision 32009-05-28 - KevinLeytonBrown

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

• Page number: 96-7 (print version)
Line: 15 to 15

• Name:Yoav
• Email:
• Content:
>
>
• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
• Email:
• Content:In Theorem 4.2.1, the text "or more players" should be dropped--finding a sample Nash equilibrium in a 3+ player game is PPAD-hard, not PPAD-complete.
-- KevinLeytonBrown - 13 Nov 2008

#### Revision 22009-04-27 - YoavShoham

Line: 1 to 1

 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

Changed:
<
<
• Page number:
• Section number:
• Date:
• Name:
>
>
• Page number: 96-7 (print version)
• Section number:4.2.2
• Page (print version):
• Date: April 27 2009
• Name:Yoav

• Email:
Changed:
<
<
• Content:
• Page number:
>
>
• Content:The tabbings are wrong in the running example of the pivoting alg
• Page number: 163 (print version)

• Section number:
Changed:
<
<
• Date:
• Name:
>
>
• Page (print version): more conceptually complicated => conceptually more complicated
• Date: April 27 2009
• Name:Yoav

• Email:
• Content:

#### Revision 12008-11-13 - KevinLeytonBrown

Line: 1 to 1
>
>
 META TOPICPARENT name="Errata"

## Chapter 4: Computing Solution Concepts of Normal-Form Games

• Page number:
• Section number:
• Date:
• Name:
• Email:
• Content:
• Page number:
• Section number:
• Date:
• Name:
• Email:
• Content:

-- KevinLeytonBrown - 13 Nov 2008

Copyright © 2008-2022 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback