I have thought about a game, however I don't really any "famous game" from the game that could illustrate this situation. I would be interested by any kind of reference about it.
The rules: The participants need to collaborate in order to keep a critical system working. Each turn, a certain amount of dollar is required to keep the system properly working. If the participants can't agree on how to pay the bill, the system break and everyone loose everything.
The individual goal is to pay the least as possible each turn for anything and profit from the others paying for the maintainance fees.
And of course the objective is to never end the game. The only solution to end it, is that every participants loose everything.
How would you describe such a system when the loss is infinite if the game stops, and the loss finite to keep it working.
Another version of this game could be a finite gain to share each month, if participants don't agree then everyone loose everything.
For what I know in the game theory, this game has the following characterics:
- Cooperative Game
- A Non-Zero Sum Game
- Infinite Game and Finite Game (The Game should continue forever, except if participants fail to find an agreement).
Bonus Question: How would you call this game in the most "game theory" way?
I just didn't find anything about a game with infine gain/loss. I would be very grateful for any reading recommendation.