  Differentiable economics uses deep learning for automated mechanism design.
Despite strong progress, it has remained an open problem to learn multi-bidder,
general, and fully strategy-proof (SP) auctions. We introduce GEneral
Menu-based NETwork (GemNet), which significantly extends the menu-based
approach of RochetNet [D\"utting et al., 2023] to the multi-bidder setting. The
challenge in achieving SP is to learn bidder-independent menus that are
feasible, so that the optimal menu choices for each bidder do not over-allocate
items when taken together (we call this menu compatibility). GemNet penalizes
the failure of menu compatibility during training, and transforms learned menus
after training through price changes, by considering a set of discretized
bidder values and reasoning about Lipschitz smoothness to guarantee menu
compatibility on the entire value space. This approach is general, leaving
undisturbed trained menus that already satisfy menu compatibility and reducing
to RochetNet for a single bidder. Mixed-integer linear programs are used for
menu transforms and through a number of optimizations, including adaptive grids
and methods to skip menu elements, we scale to large auction design problems.
GemNet learns auctions with better revenue than affine maximization methods,
achieves exact SP whereas previous general multi-bidder methods are
approximately SP, and offers greatly enhanced interpretability.
