E. H. Gerding, R. K. Dash, A. Byde and N. R. Jennings (2008) "Optimal Strategies for Simultaneous Vickrey Auctions with Perfect Substitutes", Volume 32, pages 939-982

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We derive optimal strategies for a bidding agent that participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always place non-zero bids in all available auctions, provided there are no budget constraints. With a budget, however, the optimal strategy is to bid locally if this budget is equal or less than the valuation. Furthermore, for a wide range of valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions if all auctions are identical. Finally, we address markets with both sequential and simultaneous auctions, non-identical auctions, and the allocative efficiency of the market.

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