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Chapter 2: Analyzing Games: From Optimality to Equilibrium

  • Page number: 12
    • Section number: 2.3
    • Date: 03/21/2012
    • Name: Ervin Varga
    • Email:
    • Content: One possible clarification for the expression Uwife(LW)=Uwife(WL) could be the following. Starting from the Definition 1.4.4, the left side of this equality represents the utility function over the strategy profile s, where the action profiles' first element is fixed to LW. In other words, the utility function for s when A= {(LW, LW), (LW, WL)}. The right hand side is for the case when the first element of A is fixed to WL. In both cases, the husband's mixed-strategy has Bernuolli distribution, which similarly applies to the case of a wife's mixed-strategy when the situation is reversed, i.e. Uhusband(LW)=Uhusband(WL) .
  • 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: r6 - 2012-03-21 - ErvinVarga

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