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[two_auctions] Fix conditional expectation simulation #652

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Merged
mmcky merged 2 commits into from
Oct 22, 2025
Merged

[two_auctions] Fix conditional expectation simulation #652

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[two_auctions] Fix conditional expectation simulation
oyamad Oct 21, 2025
644e9d3
minor edit
HumphreyYang Oct 22, 2025
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11 changes: 6 additions & 5 deletions lectures/two_auctions.md
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Expand Up @@ -424,13 +424,14 @@ def evaluate_largest(v_hat, array, order=1):

We can check the accuracy of our `evaluate_largest` method by comparing it with an analytical solution.

We find that despite small discrepancy, the evaluate_largest method functions well.

Furthermore, if we take a very large number of auctions, say 1 million, the discrepancy disappears.
We find that the `evaluate_largest` method functions well

```{code-cell} ipython3
v_grid = np.linspace(0.3,1,8)
bid_analytical = b_star(v_grid,N)
v_grid = np.linspace(0.3, 1, 8)
bid_analytical = b_star(v_grid, N)

# Redraw valuations
v = np.random.uniform(0, 1, (N, R))
bid_simulated = [evaluate_largest(ii, v) for ii in v_grid]

fig, ax = plt.subplots(figsize=(6, 4))
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