There is a cost associated with such deposits beyond the computational cost of the implementation. The deposit is ``in use'', and is unavailable for other purposes during the course of the auction. The precise effect of having some amount in use is dependent on the digital payment scheme being used. In an anonymous digital cash scheme, for example, it is likely to mean that the funds have been withdrawn from a (possibly interest bearing) account. In any scheme, there is an opportunity cost to having the funds in use which must be taken into account. If the overall opportunity cost to the bidders is high (e.g. if the deposit is large or if there are many bidders), this will tend to discourage bidding and depress the selling price. Therefore, compensation for the auctioneer and cost to the bidders must be balanced when choosing the value of the deposit.
One implementation on deposits is for the seller to set fixed value for all bidders as the penalty for default. The appropriate magnitude for this default penalty is highly dependent on the specific characteristics of the seller, the good, and the bidders. This method is optimal in terms of the computation and communication costs and may be the best in practice.
Another method, not detailed here, would be to have the deposit match the value of the bid. This would introduce further computational complexity, particularly since the auction is second-price and so determining the value of the deposit, even for the winning bidder, would violate privacy. An efficient method for such deposits is an open problem (see section 5) Even discounting the computational overhead, this method yields optimal results only if the total of opportunity costs of all deposits is trivial.