If either the attacker or the defender loses the test, they may attempt an Overbid Re-Test. The ‘Overbidder’, then their opponent, announces a number of Traits, up to their current maximum in the challenge attribute (Mental, Social or Physical), including the ones bid, excluding ones previously lost in challenges in previous rounds, and subtracting any penalties for negative traits identified or other circumstantial factors. A player may declare less than their current total, but cannot change their declaration during that same challenge, once made. A challenger who announced that they were expending willpower to increase their chance of success can declare three additional traits.
If the Overbidder has less traits than their opponent, the overbid fails. Otherwise a Re-Test is conducted but with the Overbidder taking a penalty to their traits equal to the number of traits their opponent bid.
At the end of the round, regardless of the success or failure of the challenge, the Overbidder loses traits equal to the number of traits their opponent bid.
This is a rule from within The Challenge System.