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An ascending-bid auction protocol with a fixed end time has been widely used at many Internet auction sites. At these sites, we can observe bidders engaging in the behavior called last minute bidding, namely, a large fraction of the bids for a good are submitted in the closing seconds of the auction. This can cause problems such as information revelation failure as well as server overload and network congestion. When bidders behave in this way, each of them cannot obtain information about the good from the other bidders' bidding behaviors, and this spoils the advantages of open-bid auctions. The result is an inefficient allocation of the good. To solve this problem, we propose a new protocol that gives each bidder an option to fix the maximum bid of a proxy agent and an incentive to submit a high bid at an early stage of an auction by paying compensation money. We examine the property of the protocol based on the game theory and clarify what situations our protocol outperforms the ordinary ascending-bid auction protocol by computer simulation.