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A chest is worth $1 per head on 20 hidden coin flips, and ten bidders submit sealed whole-dollar bids. How many pure-strategy Nash equilibria does the auction have?

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A chest's value is set by flipping 20 fair coins behind a curtain, $1 per head. Ten bidders each submit a sealed whole-dollar bid; the chest goes to a randomly chosen highest bidder, who pays their bid. How many pure-strategy Nash equilibria does the game have?

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