Resource exhaustion is perhaps the most common way for a game to reach its end. If we understand resources as those things the player has to manage while playing the game, we can see that most games have players managing the number of lives available, the amount of time left, the number of turns to play (if the number is fixed), or the choices they can make.
There are also indirect ways in which a player, through the exhaustion of resources, may be trapped in a position in which it becomes impossible for him to win the game. For example, in some first-person shooters the player has no way to inflict damage if he runs out of ammunition for all weapons. Thus, assuming that he is obliged to defeat an enemy to continue playing, he has lost the game due to the exhaustion of ammunition.
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This game uses the idea of resourse exhaustion with actual resources. In order to build a bigger base, the player must gather vespene gass along with minerals. Once you run out of these resources, it is possible to find another deposit of said resources on another portion of the map. However, if all the resources on the map become completely exhausted, the player has no way to build a bigger base, and becomes vulnerable to another player that still has resource income.
The game Gradius relies on resource exhaustion to make the game challenging. In the Japanese version of Gradius, the player has 3 lives and only 3 lives (which can be extended via points), and once the player consumes all their lives, the game is over and they must restart the game.
The Legend of Zelda: Majora's Mask
In Legend of Zelda: Majora's Mask, the game only ends when hearts are exhausted. Hearts can be collected from various in-game drops, as well as by potions and faries, but when hearts are gone, the game is over.
In Pac-Man, the player has a limited number of lives with which to play the game. Whenever a ghost touches a Pac-Man (without power pill), Pac Man loses a life. When there are no more lives to be lost, the game ends.
In the classic strategy game Sokoban, the player has to push crates (or boxes) into empty spaces. Since a box that has been backed into a corner cant be pushed out, it is possible for a player to exhaust the possible movements (ie, pushes) he can perform. If this occurs in a situation in which the boxes arent in their final (or destination) positions, the game ends.
In Diablo II, the player has a limited amount of the resource health, however even if that runs out, the character loses only the equipment he/she is carrying and re spawns in town. Since the character can continue from that point, it is simply a matter of being set back a little every time one dies and thus a player can never end the game due to resource exhaustion. In fact, with this setup, aside from the loss of currently equipped equipment, the player is not really discouraged from dying.
In Starcraft when you run out of vespene gas and crystals.You can no longer build units since it is your economical base. However, if you've amassed a large enough army, you can still win the game since victory is dependent on meeting mission goals or eliminating the enemy.
Super Monkey Balls: Banana Blitz
This game is a weak example of resource exhaustion because in the main game play, allthought you have a certain amount of lives you have started with or added to- once you have lost these lives and reach a game over- you are given the option to "continue" which starts you with the same amount of completed levels, and gives you more live. This continue option itself is never exhausted, so in a sense you never really die or run out of lives.
Warcraft III: The Frozen Throne
In Warcraft III: The Frozen Throne, if an online game lasts too long, the existing gold mines and trees can be completely mined out. These resources do not regenerate, and once this resource exhaustion is achieved, players must make do with the money/units they have to attempt to win the game. This is a weak example because the exhaustion of resources isn't directly tied to the end of the game (the game doesn't end when you run out of gold or trees), however there is a definite indirect relationship.
Gears of War
In Gears of War your health is represented by a red skull symbol that begins to appear as your character takes damage. If the symbol becomse to prominent your character dies, but if you take cover and hide your health will replenish to 100%. I believe Gears of War is a weak examples of resource exhaustion because even if you take massive amounts of damage and are about to die, you can just hide and wait and your character will recuperate his health completely. The fact that you don't have a set amount of health or lives makes Gears of War a weak examples of resource exhaustion.
Team Fortress Classic
All classes’ main weapons are firearms with a limited amount of ammunition, with arguable exception of the spy. If a player runs out of ammunition during a fire fight, they are placed into a severely disadvantaged position. If they wish to continue fighting their opponent, they will have to resort to melee weapons, which are significantly weaker than their main weapons. At that point, with depleted resources, the player is practically considered dead.