Auction theory is of central importance in the study of markets. Unfortunately, we do not know equilibrium bidding strategies for most auction games. For realistic markets with multiple items and value interdependencies, the Bayes Nash equilibria (BNEs) often turn out to be intractable systems of partial differential equations. Previous numerical techniques have relied either on calculating pointwise best responses in strategy space or iteratively solving restricted subgames. The paper presented in this Virtual Market Design Seminar presents a learning method that represents strategies as neural networks and applies policy iteration on the basis of gradient dynamics in self-play to provably learn local equilibria. Their empirical results show that these approximated BNEs coincide with the global equilibria whenever available. The method follows the simultaneous gradient of the game and uses a smoothing technique to circumvent discontinuities in the ex post utility functions of auction games. Discontinuities arise at the bid value where an infinite small change would make the difference between winning and not winning. Convergence to local BNEs can be explained by the fact that bidders in most auction models are symmetric, which leads to potential games for which gradient dynamics converge.
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The seminar presentations are scheduled to last 60 minutes: 45 minutes of presentation and 15 minutes for both comments and questions.
We will experiment with various methods for questions: A moderator collects questions during the presentation. Speakers will be encouraged to pause every few slides to allow a gap for questions. The moderator will relay clarification questions or unmute selectively during the talk. Remaining questions will be collected and asked in the discussion period.
Just like with other initiated virtual seminars, these rules are subject to change as we gain experience with how to handle the seminar most efficiently.
The Virtual Market Design Seminar is an open online alternative to seminars cancelled due to the COVID-19. Seminars will cover all fields from market design. The seminar presentations are scheduled to last 60 minutes, after 45 minutes of presentation, 15 minutes are for both comments and question.