Figure 8
From: Designing all-pay auctions using deep learning and multi-agent simulation
Bidder CDF comparison. (a) shows the CDFs for each of five different auction designs assuming the bidder plays the Nash distribution. The first prize is listed in the legend; the second prize equals one minus the first; no prize is given to the third bidder. The remaining plots compare the Nash CDF with the CDF learned by Fictitious Self-Play for different first prize amounts. (b)–(f) Show the effect of training iterations and discretization granularity on the final CDF. The arrow in (c) highlights a common trend where the CDF converges to Nash from above as a finer discretization is introduced: coarser discretizations lead to under bidding and, in turn, underestimates of the auctioneer utility. (d) Shows that increasing training iterations reduces error, but in a less structured manner than bid granularity.
