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Upstart Puzzles: Auction Triplets


Auction Triplets, illustration

Credit: Andrij Borys Associates / Shutterstock

There are objects of four types and n people, each with a budget of $99. The objective of each one is to acquire three objects of the same type (any type) before anyone else does; for example, if player A acquires three type 1 objects before any other player acquires any three objects of any type, A wins. Assume each auction is resolved through a highest-bid method; that is, the highest bidder pays the amount he or she bids (Vickrey auctions are a possible variant.) Every bid must be an integral number of dollars. If there is a tie, the bidder (if any) who won the immediately preceding auction gets the item if that bidder is one of those who tied. In every other case, the tie ends in a draw, and nobody takes the item in that auction.

By symmetry, there cannot be a guaranteed winning strategy, but the general challenge is to work out probabilistically good strategies, given knowledge of the sequence of item types to be auctioned.


 

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