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.