A gaming system and method including a plurality of gaming devices that may participate in a shared secondary or bonus game and a controller operable to communicate with said plurality of gaming devices. At least one of the plurality of gaming devices is programmed to generate and accumulate collectors upon an occurrence of a first triggering event. Upon an occurrence of a second triggering event at one of the gaming devices, the controller enables a player of said gaming device to redeem a quantity of accumulated collectors in a bonus event. The controller also enables the player to invite other gaming devices from the plurality of gaming devices to redeem accumulated collectors and participate in said bonus event. The odds of each player earning a higher-valued total award in the bonus event increases with the total number of accumulated collectors redeemed in the bonus event.