Searching for a subfield of game theory related to repeated games and games with random time horizons.
Specifically:
- Multiple, repeated games
- Each game of some finite, yet unknown length to the participants (it might end next turn)
I believe this would be something like "repeated differential games" or "repeated differential games with random time horizons"
However, what I have found does not appear to correspond:
- Repeated Games With Differential Time Preferences - Players who have different time horizons for benefits
- Repeated Games and Qualitative Differential Games - Repeated games where players cannot win, only try to cause a "trajectory to remain in a certain set"
- Group and Individual Play in a Sequential Market Game and the Effect of the Time Horizon - Group and individual choices in markets, time horizon is difference between one-shot and many interactions
- Stochastic Differential Games and Energy-Efficient Power Control - Stochastic Game of power system balancing where players effectively have infinite turn horizon
However, none of these are really what I'm attempting to find.
An example of what I'm attempting to find would be:
- Many basketball teams playing each other
- Each game they play is of a predetermined, yet unknown length to the players
- It might be 10 minutes, it might be 2 hours, except you can't change your strategy because you know its 5 minutes from the buzzer.
- The teams play many matches against each other (such as a league).
- There is some concept of a "score" or relative performance in an individual game.
Could also be individuals, such as tennis players, I'm not necessarily set on group vs individual. This seems like it would also have relevance to military or political games, with many games of many unknown length rounds, where you never know when your "score" will be checked.
Specific question would be: what is this subfield, if it exists or has a known term? Perhaps papers, as GScholar seems to be letting me down.