I am new to game theory, I want to know if a Nash equilibrium exists for a game having the following properties:
- Finite number of players
- The strategy space for each player is R^2 (R for real numbers)
- The utility function could have infinite values (notably, the utility function of an individual for a chosen strategy is infinite if a certain constraint depending on the strategies chosen by others is not satisfied)
I know that the problem can be formulated in a generalized game framework, but the difference here is that I accept strategies with infinite utility value if and only if it is the only possible choice for the player.
Can anyone help please?
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