<P> The strategy of overbidding is dominated by bidding truthfully . Assume that bidder i bids b i> v i (\ displaystyle b_ (i)> v_ (i)). </P> <P> If max j ≠ i b j <v i (\ displaystyle \ max _ (j \ neq i) b_ (j) <v_ (i)) then the bidder would win the item with a truthful bid as well as an overbid . The bid's amount does not change the payoff so the two strategies have equal payoffs in this case . </P> <P> If max j ≠ i b j> b i (\ displaystyle \ max _ (j \ neq i) b_ (j)> b_ (i)) then the bidder would lose the item either way so the strategies have equal payoffs in this case . </P> <P> If v i <max j ≠ i b j <b i (\ displaystyle v_ (i) <\ max _ (j \ neq i) b_ (j) <b_ (i)) then only the strategy of overbidding would win the auction . The payoff would be negative for the strategy of overbidding because they paid more than their value of the item, while the payoff for a truthful bid would be zero . Thus the strategy of bidding higher than one's true valuation is dominated by the strategy of truthfully bidding . </P>

What was an auction where the highest bidder wins