[two_auction] Lecture review with math and warning fixes

[HumphreyYang]

This PR:

• Fixes warnings in Python warnings found in code output #548
• Update code to PEP8
• Fix mathos and typos
• Reformat subtitles according to style guide.

[github-actions]

🚀 Deployed on https://68a282df2f56647b258723db--nostalgic-wright-5fa355.netlify.app

[HumphreyYang]

Hi @mmcky, this PR fixes the python warning mentioned in #548.

There are a few lectures using JAX that has cache build failure as shown in the statistics that is related to the CuDNN version of the builder.

For instance, mccall_model_with_separation:

2025-08-17 11:10:22.824448: E external/xla/xla/stream_executor/cuda/cuda_dnn.cc:466] Loaded runtime CuDNN library: 9.5.1 but source was compiled with: 9.8.0.  CuDNN library needs to have matching major version and equal or higher minor version. If using a binary install, upgrade your CuDNN library.  If building from sources, make sure the library loaded at runtime is compatible with the version specified during compile configuration.
2025-08-17 11:10:22.827370: E external/xla/xla/stream_executor/cuda/cuda_dnn.cc:466] Loaded runtime CuDNN library: 9.5.1 but source was compiled with: 9.8.0.  CuDNN library needs to have matching major version and equal or higher minor version. If using a binary install, upgrade your CuDNN library.  If building from sources, make sure the library loaded at runtime is compatible with the version specified during compile configuration.
2025-08-17 11:10:22.879136: E external/xla/xla/stream_executor/cuda/cuda_dnn.cc:466] Loaded runtime CuDNN library: 9.5.1 but source was compiled with: 9.8.0.  CuDNN library needs to have matching major version and equal or higher minor version. If using a binary install, upgrade your CuDNN library.  If building from sources, make sure the library loaded at runtime is compatible with the version specified during compile configuration.
2025-08-17 11:10:22.888317: E external/xla/xla/stream_executor/cuda/cuda_dnn.cc:466] Loaded runtime CuDNN library: 9.5.1 but source was compiled with: 9.8.0.  CuDNN library needs to have matching major version and equal or higher minor version. If using a binary install, upgrade your CuDNN library.  If building from sources, make sure the library loaded at runtime is compatible with the version specified during compile configuration.

Please let me know your thoughts when you have time!

EDIT: False Alarm

[Copilot]

Pull Request Overview

This PR fixes warnings, improves code formatting, and corrects mathematical expressions and typos in the two auctions lecture. The changes focus on bringing the code up to PEP8 standards while fixing several content issues.

Key changes:

• Fixed mathematical error in surplus value calculation (line 77)
• Corrected spelling errors including "Wikepedia" to "Wikipedia" and "randomess" to "randomness"
• Reformatted code to follow PEP8 standards with proper spacing and line breaks

---

_{You can also share your feedback on Copilot code review for a chance to win a $100 gift card. Take the survey.}

[mmcky]

mccall_model_with_separation

@HumphreyYang thanks for this PR.

I'm not seeing the issue you mention re: CUDANN in:

https://68a1338ff9648626d407c819--nostalgic-wright-5fa355.netlify.app/mccall_model_with_separation.html

is that the correct place to be looking? In the preview?

[HumphreyYang]

mccall_model_with_separation

@HumphreyYang thanks for this PR.

I'm not seeing the issue you mention re: CUDANN in:

https://68a1338ff9648626d407c819--nostalgic-wright-5fa355.netlify.app/mccall_model_with_separation.html

is that the correct place to be looking? In the preview?

Thanks @mmcky, my bad, it's a false alarm. I was looking at the build on my end and confused it with the preview.

My CuDNN needs an upgrade : )

[mmcky]

thanks @HumphreyYang for the PR. LGTM.