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Chapter 2: Analyzing Games: From Optimality to Equilibrium

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  • Page number:12
    • Section number:2.3
    • Date:3/13/12
    • Name:Julian Fogel
    • Content:The expression $U_{wife}(LW)$ is not precisely defined. The reader is left to guess what it refers to exactly. My guess is that we could define $u_{(i,-j)}$ in a similar fashion as $s_{-j}$, and that $U_{wife}(LW)$ is $u_{(1,-2)}(LW)$.
  • Page number:10
    • Section number:2.2
    • Date:3/13/12
    • Name:Julian Fogel
    • Content:Writing $s=(s_i,s_{-i})$ contradicts the definition that $s$ is a member of the Cartesian product $S_1X...XS_n$. The order in a Cartesian product matters, as does nesting. $(s_i,s_{-i})$ is a member of $S_iX(S_1X...S_{i-1}XS_{i+1}X...XS_n)$ which is not the same as $S_1X...XS_n$.This may especially lead to confusion in the case of 2-player games, when $i=2$ since the order of the first and second player gets swapped: $s = (s_i,s_{-i}) = (s_2,s_1)$. But we also have by definition that $s = (s_1,s_2)$.

The following error was fixed in version 1.1:

  • Page number: 11
    • Section number: 2.2
    • Date: 11/26/08
    • Name: Kevin Leyton-Brown
    • Email:
    • Content: Definitions 2.2.3 and 2.2.4 are each missing a few words. 2.2.3 should read "A strategy profile s = (...) is a strict Nash equilibrium if ...". Similarly, 2.2.4 should read "A strategy profile s = (...) is a weak Nash equilibrium if ...".
-- KevinLeytonBrown - 21 Nov 2008
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Topic revision: r5 - 2012-03-13 - JulianFogel

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