One embodiment provides a gaming system having a plurality of gaming devices. Each of the gaming devices enables a player to make wagers on plays of a primary game. For each gaming device, for each occurrence of a designated accumulation outcome, the player of that gaming device accumulates one or more positions on a bonus game display matrix. When a bonus game trigger occurs, the triggering gaming device is identified. In the bonus game, a plurality of symbols are displayed in the plurality of positions of the bonus game display matrix. The player of the triggering gaming device is provided with any awards associated with any winning symbol combinations formed by the displayed symbols. Additionally, for each assigned position of the bonus game display matrix that displays a symbol which is part of a winning symbol combination, a participation award is provided to the player assigned to that position.