## Chapter 5: Games with Sequential Actions: Reasoning and Computing with the Extensive Form

• Page number: 115
• Section number:5.1.2
• Content: In Definition 5.1.2, pure strategies as defined are products of the set of all actions available at all choice nodes owned by a player, rather than products of actions available at all chocie nodes owned by a player. To correct this, change $\prod_{h \in H, \rho(h = i)} \chi(h)$ to $\prod_{h \in H, \rho(h) = i, a \in \chi(h)} a$
• --
• Page number:
• Section number:5.1.4
• Date:8/6/2010
• Name:Kevin
• Content:In Figure 5.7, change the "forall" to "for". (Under the previous wording, it is possible to understand that the different iterations are executed in parallel rather than sequentially.)
• Page number: 139
• Section number:5.2.4
• Date:5/5/2020
• Name:Brian Lunday
• Email: brian[dot]lunday[at]afit[dot]edu
• Content:In Definition 5.2.10 (Sequential equilibrium), in the first condition, the limit should be as "m -> \infty'' instead of ''n-> \infty".
• Page number: 139
• Section number:5.2.4
• Date:5/5/2020
• Name: Brian Lunday
• Email: brian[dot]lunday[at]afit[dot]edu
• Content:In Definition 5.2.10 (Sequential equilibrium), in the second condition, the right hand side of the inequality should reference index the alternative strategy s' for player i, writing it as s'_i.
• Page number:136-142
• Section number:5.2.3
• Date:4/4/2014
• Content:After Definition 5.2.8 (until the end of section 5.2.3), the book keeps using "I" to refer to a certain information set in "I_i" (for player i), but earlier in the book in Definition 5.2.1 the book defined I to be the tuple of the information sets of n players (namely, I = (I_1, I_2, ..., I_n)). This may lead to a huge change, but just to be consistent with the rest of the chapter, it might be wise to call it "I_{i, j}" or "I_{i, k}" (or such) instead of just "I".

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

• Page number: 144
• Section number: 5.2.4
• Date: 11/26/08
• Name: James Wright
• Email: jrwright@csDELETEthisTEXT.ubc.ca
• Content: Theorem 5.2.12 should read "In extensive-form games of perfect information, the set of subgame-perfect equilibria is exactly the set of sequential equilibria," and footnote 9 should be removed. (The issue with genericity arises only under games of imperfect information.)
• Page number: 132
• Section number: 5.2.2
• Date: Feb 10, 2009
• Name: Sean Sutherland
• Email: ssuther(at) cs.ubc.ca
• Content: The paragraph beginning "We illustrate this distinction first..." should be removed. We discussed that it could be misleading about the differences between behavioral and mixed strategies, while not really contributing something worthwhile. One point was that it doesn't mention that correlations in mixed strategies only occur off-path.
• Page number: 125
• Section number: 5.1.5
• Date:May 13, 2009
• Name: Grigorios Tsoumakas
• Email: greg@csdDELETEthisTEXT.auth.gr
• Content:"from the root of the tree up to the root" should be "from the leaves of the tree up to the root"
• Page number: 133
• Section number:5.2.3
• Date:Feb19, 2010
• Name B.J.Buter
• Email: bjbuter [at] science [dot] uva [dot] nl
• Content: Definition 5.2.3, using n as a counter is confusing since in other definitions n indicates the number of players.
• Page number: 130
• Section number:5.2.1
• Date:Feb 18, 2010
• Name: B.J.Buter
• Email: bjbuter [at] science [dot] uva [dot] nl
• Content: Definition 5.2.1 "I=..., equivalence relation" is not an equivalence relation. An equivalence relation is a collection of ordered pairs, thus if I_{i,j} were a relation, then where h \in I_{i,j} is written, h should be an ordered pair, this is not meant. I would rewrite as:"I=(I_1,...,I_n), where I_i={I_{i,1},...,I_{i,k_i}} is a partition of \{h\in H : \rho(h) = i\}, with I_{i,j} equivalence classes."
• Page number: 133
• Section number:5.2.3
• Date:Feb19, 2010
• Name B.J.Buter
• Email: bjbuter [at] science [dot] uva [dot] nl
• Content: Definition 5.2.3, item 2 equivalence classes are only defined for nodes where a player acts, according to definition 5.2.1. The restriction if \rho(h_j)=i should be added.
• Page number: 137-138
• Section number:5.2.4
• Date:Feb 27, 2010
• Name:Nicolas Lambert
• Content:All instances of S should be replaced by s for consistency with the rest of the book.
-- KevinLeytonBrown - 13 Nov 2008
Topic revision: r13 - 2020-05-05 - BrianLunday

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