A gaming system where, as players place wagers to play the primary games of the gaming devices, a portion or percentage of the wager placed by each player to initiate the primary game is allocated to an accumulated value pool. A target value is based on the average expected payout of a bonus event. In one embodiment, if the accumulated value pool meets or exceeds the target value, a bidding sequence is triggered. During the bidding sequence, the central controller enables each of the players playing at the gaming devices to place one or more bids for the opportunity to participate in the bonus event. In one embodiment, the player who places the highest bid participates in the bonus event and is provided with a bonus award, wherein the bonus award may be equal to, higher than, or lower than the winning bid.