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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 5: AAAI-22 Technical Tracks 5

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games

February 1, 2023

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Authors

Kai Wang

Harvard University


Lily Xu

Harvard University


Andrew Perrault

The Ohio State University


Michael K. Reiter

Duke University


Milind Tambe

Harvard University


DOI:

10.1609/aaai.v36i5.20457


Abstract:

A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium. Standard approaches for computing equilibria in these games reformulate the followers' best response as constraints in the leader's optimization problem. These reformulation approaches can sometimes be effective, but make limiting assumptions on the followers' objectives and the equilibrium reached by followers, e.g., uniqueness, optimism, or pessimism. To overcome these limitations, we run gradient descent to update the leader's strategy by differentiating through the equilibrium reached by followers. Our approach generalizes to any stochastic equilibrium selection procedure that chooses from multiple equilibria, where we compute the stochastic gradient by back-propagating through a sampled Nash equilibrium using the solution to a partial differential equation to establish the unbiasedness of the stochastic gradient. Using the unbiased gradient estimate, we implement the gradient-based approach to solve three Stackelberg problems with multiple followers. Our approach consistently outperforms existing baselines to achieve higher utility for the leader.

Topics: AAAI

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HOW TO CITE:

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games Proceedings of the AAAI Conference on Artificial Intelligence (2022) 5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games AAAI 2022, 5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe (2022). Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games. Proceedings of the AAAI Conference on Artificial Intelligence, 5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. 2022. Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games. "Proceedings of the AAAI Conference on Artificial Intelligence". 5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. (2022) "Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games", Proceedings of the AAAI Conference on Artificial Intelligence, p.5219-5227

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe, "Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games", AAAI, p.5219-5227, 2022.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. "Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. "Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 5219-5227.

Kai Wang||Lily Xu||Andrew Perrault||Michael K. Reiter||Milind Tambe. Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games. AAAI[Internet]. 2022[cited 2023]; 5219-5227.


ISSN: 2374-3468


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Copyright 2022, Association for the Advancement of
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