Alice and Bob are at a strange auction. The item up for auction is $20. The rules

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Alice and Bob are at a strange auction. The item up for auction is $20.

The rules are that no one can bid twice in a row and that the highest bidder gets the $20. Also, and this is very strange, the highest bidder and the next highest bidder have to pay their bids. For example, if Bob bids $5, Alice bids $6, and Bob then passes, Alice gets the $20 and pays $6 to the auctioneer and Bob pays the auctioneer $5. Both have $100 to bid. What is the optimal strategy?

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