Winner's curse arises in cases where several bidders in an auction are unaware of the true value of the object. In this auction, the most optimistic of the bidders will bid the most for the object. Unfortunately, for the bidder --- the best estimate of the value of the object is the average of the bids. Since the winning bidder bids more than the average bid, the winner overpays for the object and is "cursed". If the bidders "know that they do not know" the value of the object, then they have an incentive to shade down their bid.
The New York Times has a nice piece about the Nash Game that cities are now playing as they position to attract the new Amazon HQ. A few thoughts. First, the counter-factual; in the absence of local government incentives where would Amazon HQ locate? Second, what ex-ante economic model do cities use to predict how aggressively they should bid for the Amazon HQ. For example, suppose that Chicago offers $2 billion dollars worth of tax cuts. It must be the case that some economic consulting firm has a model predicting that if Chicago lures the Amazon HQ that this will generate more than $2 billion in new income for the economy. But, what model did the consultants use? Is it a simple input/output model? How does this economic consulting firm know how the Chicago's counter-factual path would be affected by attracting the HQ?
I would point my readers to my 2017 JUE paper for some insights on economic agglomeration where we study the impact of new industrial parks in China on the local economy.
A final point is for the local mayors to consider Tim Bartik's finding from his 1991 Upjohn book. When states attract a big factory, the jobs do not go to the incumbent unemployed or to those out of the labor force, instead new migrants move in and gain the bulk of the jobs. So, if a mayor seeks to trigger a "brain importing" then the Amazon HQ luring effort makes more sense.
In a Nash game, everyone would be better off if they could commit to co-operate but this is not a nash equilibrium. Richard Florida has an excellent piece published here exploring the point that the efficient allocation of resources is unlikely to be an equilibrium in this case.