Gaming system and method providing a multiple-player bonus redemption game

A gaming system comprising:

• at least one processor;
• and
• at least one memory device which stores a plurality of instructions, which when executed by the at least one processor, causes the at least one processor to:
• upon each occurrence of a first triggering event, accumulate at least one collector for at least one of a pluralty of players at at least one of a plurality of gaming devices, wherein each gaming device enables the player at said gaming device to place at least one wager on at least one pla of at least one primary game;
• and
• upon an occurrence of a second triggering event:
• enable a first one of the players at a first one of the gaming devices to redeem a quantity of accumulated collectors in a secondary game,
• cause a display of an indication of a plurality of other players that have accumulated collectors to be displayed to the first one of the players,
• after causing a display of an indication of said other players that have accumulated collectors, enable the first one of the players to invite at least a second one of the players at a second one of the gaming devices to redeem accumulated collectors in the secondary game, and
• cause any awards associated with the redeemed collectors to be displayed.

A gaming system comprising:

• at least one processor;
• and
• at least one memory device which stores a plurality of instructions, which when executed by the at least one processor, causes the at least one processor to:
• upon each occurrence of a first triggering event, accumulate at least one collector for at least one of a plurality of players at at least one of a plurality of gaming devices, wherein each gaming device enables the player at said gaming device to place at least one wager on at least one play of at least one primary game;
• and
• upon an occurrence of a second triggering event:
• enable a first one of the players at a first one of the gaming devices to invite at least a second one of the players at a second one of the plurality of gaming devices to participate in a secondary game,
• enable the first one of the players to input to cancel or participate in the secondary game,
• if the first one of the players inputs to participate in the secondary game:
• enable each participating player in the secondary game to redeem a quantity of accumulated collectors associated with that player,
• determine any awards for the collectors redeemed in the secondary game, and
• for each participating player in the secondary game, cause a display of a total award based on the determined awards for the redeemed collectors associated with that player, and
• if the first one of the players inputs to cancel the secondary game, enable each player to retain any accumulated collectors associated with that player.

A gaming system comprising:

• at least one processor;
• and
• at least one memory device which stores a plurality of instructions, which when executed by the at least one processor upon an occurence of a triggering event, causes the at least one processor to:
• enable each of a plurality of players at each of a plurality of gaming devices to participate in a competition secondary game, wherein each gaming device enables the player at said gaming device to place at least one wager on at least one play of at least one primary game, and
• determine any awards for the competition secondary game, wherein the greater the quantity of players that participate in the competition secondary game, the higher the probability that a designated award will be provided to at least one of said players in association with said competition secondary game.