Chapter 3: Introduction to Noncooperative Game Theory: Games in Normal Form

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

• Page number: 52
  • Section number: Theorem 3.1.8 (Proof)
  • Date: 5 Feb 2009
  • Name: Nimalan Mahendran
  • Email: nimalan@csDELETEthisTEXT.ubc.ca
  • Content: The portion of the proof for the trivial case where the agent is indifferent should set u(.) = 0 for all outcomes and lotteries over outcomes. Part 2 is then immediate - decomposability is never used.
• Page number: 52
  • Section number: Theorem 3.1.8 (Proof)
  • Date: 5 Feb 2009
  • Name: Nimalan Mahendran
  • Email:nimalan@cs.ubc.ca
  • Content:o1 indiff l1 strict_pref l2 indiff o2 need only follow from transitivity and completeness.
• Page number: 71
  
  • Section number: Theorem 3.3.22 (Nash, 1951)
  • Date: 5 Feb 2009
  • Name: Nimalan Mahendran
  • Email:nimalan@cs.ubc.ca
  • Content:Notation: u_i(a_i, s_{-i}) represents i's utility of playing action a_i given everyone else played s_{-i}. The last paragraph of the proof contains the following notation, which is inconsistent: u_{i, a'_i}(s). This should be u_i(a'_i, s_{-i}).
• Page number: 52
  • Section number:Theorem 3.1.8 (Proof), Part 1
  • Date:6 Feb 2009
  • Name:Nimalan Mahendran
  • Email:nimalan@cs.ubc.ca
  • Content:In the first line of part 1, lottery l_1 should be [u(o_1) : o_overbar; 1 - u(o_1) : o_underbar] and similarly for l_2. Otherwise, (u(o_1) + (1 - u(o_2) = 1) does not necessarily hold, making it an invalid lottery. Also, the definition seems to follow (for me, at least) from the previous paragraph where it says o_i \indiff [u(o_i) : o_overbar; (1 - u(o_i)) : o_underbar].
• Page number: 52
  • Section number: Theorem 3.1.8
  • Date: June 19 2009
  • Name: Nicolas Dudebout
  • Email:
  • Content: The utility function should be defined not only over the finite set O but also over all the lotteries on O. Else, the LHS of Part 2 is not defined.
• Page number: 83
  • Section number: 3.4.6
  • Date: Feb 27, 2010
  • Name: Kevin
  • Content: Changed the definition of trembling-hand perfect equilibrium to use notation consistent with the rest of the book: "A mixed-strategy profile $s$ is a (trembling-hand) perfect equilibrium of a normal-form game $G$ if there exists a sequence $s^0, s^1, \ldots$ of fully mixed-strategy profiles such that $\lim_{n\rightarrow\infty}s^n=s$, and such that for each $s^k$ in the sequence and each player $i$, the strategy $s_i$ is a best response to the strategies $s_{-i}^k$."

-- KevinLeytonBrown - 13 Nov 2008