# Difference: ComputingNormalFormErrata (1 vs. 15)

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

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

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• 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

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

• Page number: 95 (first edition)
• Section number: 4.2.2
• Date: May 2, 2020
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• Name: Brian L.
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• 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

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

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• Page number: 97 (first edition)
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• 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

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

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• 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).
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• 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.

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• 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
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-- KevinLeytonBrown - 13 Nov 2008
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-- KevinLeytonBrown - 13 Nov 2008

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

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

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• 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).

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• Section number:
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• 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
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-- KevinLeytonBrown - 13 Nov 2008
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-- KevinLeytonBrown - 13 Nov 2008
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#### Revision 102010-03-04 - KevinLeytonBrown

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

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• 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:
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• 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."
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• 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

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

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• 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."
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• 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

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

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• 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:
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### 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
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• Name:Yoav
• Email:
• Content:The tabbings are wrong in the running example of the pivoting alg
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• 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

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

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• Name:Yoav
• Email:
• Content:
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-- KevinLeytonBrown - 13 Nov 2008
\ No newline at end of file
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• 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

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 META TOPICPARENT name="Errata"

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

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• 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:
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• 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

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 META TOPICPARENT name="Errata"

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

• Page number: 96-7 (print version)
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• Date: May 28 2009
• Name:Kevin
• Section: 4.2.1
Changed:
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• 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."
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• 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

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 META TOPICPARENT name="Errata"

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

• Page number: 96-7 (print version)
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• Page number: 92 (electronic version)
• Date: May 28 2009
• Name:Kevin
Changed:
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• 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.
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• 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

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 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:
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• 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

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

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

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

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• Page (print version): more conceptually complicated => conceptually more complicated
• Date: April 27 2009
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#### Revision 12008-11-13 - KevinLeytonBrown

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 META TOPICPARENT name="Errata"

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

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-- KevinLeytonBrown - 13 Nov 2008

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