## 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
• Date: May 2, 2020
• 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)
• 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: 114 (electronic version)
• Section number: 4.6 (Theorem 4.6.1)
• Date: March/10/2015
• Name: Haden Lee
• Email:haden[dot]lee[at]cs[dot]stanford[dot]edu
• 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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### 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
• 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

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Topic revision: r15 - 2020-05-28 - LeiZhou

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