---++ Chapter 2: Analyzing Games: From Optimality to Equilibrium * *Page number: 12* * Section number: 2.3 * Date: 03/21/2012 * Name: Ervin Varga * Email: e.varga@ieee.org * Content: One possible clarification for the expression U<sub>wife</sub>(LW)=U<sub>wife</sub>(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. U<sub>husband</sub>(LW)=U<sub>husband</sub>(WL) . * *Page number:12* * Section number:2.3 * Date:3/13/12 * Name:Julian Fogel * Email:filos2@yahoo.com * 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 * Email:filos2@yahoo.com * 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 $s = (s_1,s_2)$. * *Page number: 9* * Date: 2017-01-31 * Name: Ulle Endriss * Content: "In this section" should be "In this chapter" --- _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: kevinlb@cs.ubc.ca * 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 ...". -- Main.KevinLeytonBrown - 21 Nov 2008
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