diff options
Diffstat (limited to 'ps1')
| -rw-r--r-- | ps1/main.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/ps1/main.tex b/ps1/main.tex index 5ee2ece..35ad24b 100644 --- a/ps1/main.tex +++ b/ps1/main.tex @@ -166,7 +166,7 @@ is a Bayes-Nash equilibrium yet because it is not onto. However, we can show that bids which are not attained by $s$ are dominated. Since $s$ is non-decreasing, its maximum value is: \begin{displaymath} -s^* = \frac{w_1-w_2}{w_1}\int_{\R^+} zf(z)dz} +s^* = \frac{w_1-w_2}{w_1}\int_{\R^+} zf(z)dz \end{displaymath} Let us show that bids above $s^*$ are dominated by $s^*$. The utility of an agent with value $v$ when bidding $s^*$ is $u = w_1\big(v-s^*\big)$ since he @@ -351,7 +351,7 @@ By the central limit theorem, $X_n$ converges in distribution: \end{displaymath} Note that: \begin{displaymath} - \E\left[I_nX_n] = \E\left[h(X_n)\right] + \E[I_nX_n] = \E\left[h(X_n)\right] \end{displaymath} where $h(x) = \mathbf{1}_{x\geq 0}$ is the indicator function of $x$ being non-negative. Using convergence in distribution: |