International Escalation and the Dollar Auction

Two players bid for a dollar on the condition that both the loser and the winner must pay the bids, although only the winner will receive the dollar. Collusion or threats are excluded; bids must be in units of nickels; and a player does not bid in a situation in which bidding and not bidding would lead to the same payoff. We derive a formula for the players' rational strategies, which implies, for example, that when both have $2.50 available, the first bidder should open by bidding $.60 and the other should remain silent. The fact that rational players would not bid against each other shows that unlike the Prisoners' Dilemma, the dollar auction is not innately a trap, but exploits some irrationality in the bidders' behavior. The dollar auction resembles international escalation in that the governments in conflict commit resources that will not be returned. Some points of difference in the two situations are listed and discussed.