  Bidding in simultaneous auctions is challenging because an agent's value for
a good in one auction may depend on the uncertain outcome of other auctions:
the so-called exposure problem. Given the gap in understanding of general
simultaneous auction games, previous works have tackled this problem with
heuristic strategies that employ probabilistic price predictions. We define a
concept of self-confirming prices, and show that within an independent private
value model, Bayes-Nash equilibrium can be fully characterized as a profile of
optimal price prediction strategies with self-confirming predictions. We
exhibit practical procedures to compute approximately optimal bids given a
probabilistic price prediction, and near self-confirming price predictions
given a price-prediction strategy. An extensive empirical game-theoretic
analysis demonstrates that self-confirming price prediction strategies are
effective in simultaneous auction games with both complementary and
substitutable preference structures.
