I am trying to understand how to compute all Nash equilibria in a 2 player game, but I fail when there are more than 2 possible options to play. Could somebody explain to me how to calculate a matrix like this (without computer) \begin{matrix} 1,1 & 10,0 & -10,1 \\ 0,10 & 1,1 & 10,1 […]

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all $\frac{I}{J}$-subsets of $\cal I$ contains exactly $N=\binom{I}{\frac{I}{J}}$ elements. Now, consider the set $Y_{I,J}$ of all permutations of $X_{I,J}$, viewed as columns enumerating the […]

I am having trouble understanding a second price auction with a reserve price, i.e. a second price auction where each player’s valuation is uniformly distributed on $[0, 1]$, and the two valuations are independent random variables. Here we have a fixed reserve price $r$ > 0 that is common knowledge with the buyers: if the […]

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