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Difficulty: Hard
Category: Game Theory & Logic
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Topics: game-theory, bayesian-nash, auction, incomplete-information, probability
In a sealed-bid auction, two bidders are competing for an item. Bidder 1's valuation of the item, $v_1$ , is known to both bidders. Bidder 2's valuation, $v_2$ , is private information, and Bidder 1 only knows that $v_2$ is uniformly distributed on the interval $0, 100$. Assume that both bidders are risk-neutral and seek to maximize their expected profit. Bidders submit bids simultaneously. What characterizes a Bayesian Nash Equilibrium in this auction?
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