New conversational chess notebook using nested chats and tool use

[ekzhu]

Why are these changes needed?

The existng conversational chess notebook uses complicated register_reply and subclassing.

Replace it with a new notebook using nested chat and tool use.

Related issue number

Checks

• I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://microsoft.github.io/autogen/docs/Contribute#documentation to build and test documentation locally.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 35.20%. Comparing base (c8aca8d) to head (ad83c53).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2137      +/-   ##
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- Coverage   36.77%   35.20%   -1.58%     
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  Files          69       69              
  Lines        7133     7133              
  Branches     1556     1556              
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- Hits         2623     2511     -112     
- Misses       4277     4398     +121     
+ Partials      233      224       -9     

Flag	Coverage Δ
unittests	35.18% <ø> (-1.58%)	⬇️

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[gagb]

Looks good.

Some suggestions for improvement:

• Clarify what happens when the conversation between a player_a and board proxy ends. E.g., how are the results from that conversation are transformed into a message to player_b.
• At some point in the notebook, the logs show an empty carryover message. Consider explain what carryover does in the chess scenario.
• Emphasize its important to use the board proxy (or at least a board proxy that use the same board object), to ensure a shared state (beyond chat history) between the players

@ekzhu do you think this is the simplest way to implement this scenario with AutoGen? If no, clarify that this is not a design recommendation for optimal implementation but an illustrative example.

[ekzhu]

Clarify what happens when the conversation between a player_a and board proxy ends. E.g., how are the results from that conversation are transformed into a message to player_b.

Done. Explained with updated figure.

At some point in the notebook, the logs show an empty carryover message. Consider explain what carryover does in the chess scenario.

Done

Emphasize its important to use the board proxy (or at least a board proxy that use the same board object), to ensure a shared state (beyond chat history) between the players

Done

@ekzhu do you think this is the simplest way to implement this scenario with AutoGen? If no, clarify that this is not a design recommendation for optimal implementation but an illustrative example.

I believe this is it. It should be the example we show to illustrate how to use nested chat with tool use. I have also updated related tutorial chapters.