Signalling/Auctions Watch

1. Could anyone give me a nudge in the right direction with the following question? Thanks.

Consider the following model of the winner's curse: At an auction an item with some objective, but unknown value xtrue is up for sale. There are just two bidders. Each of the bidders gets some signal x1 (bidder 1), x2 (bidder 2) about xtrue. Both bidders know this and also know that their signals are distributed as follows: With probability 0.5 the signal is xi = xtrue + 1 and with probability 0.5 the signal is xi = xtrue - 1. Both bidders are risk-neutral. If both are prepared to bid up to the same value then assume that a coin flip determines which bidder gets the object at that bid.

(a) Suppose the signals are independent of each other and both bidders know this. What is the highest bid bidder 1 should be willing to bid up to?

(b) Answer the same question as above but now assume that both bidders receive the same signal x. (So rather than being independent the signals are now perfectly correlated).

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Updated: December 13, 2010
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