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I'm new to game theory. So far, I know that we have games with finite strategy sets and games with continuous strategy sets. I was wondering if there are any games in which some players have finite strategies, while some others have continuous strategies, e.g. some bounded interval.

I searched for hybrid games, but it seems this is not the keyword.

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  • $\begingroup$ I believe in the literature, they use the word finite. $\endgroup$
    – Has
    Commented Sep 27, 2020 at 12:08
  • $\begingroup$ of course, they do. In the most general form agents have a cost function $f_{i}(x)$, an action set $\Omega_{i}$, and coupling constraints $g(x) \leq 0$ where $x$ is the action/strategy profile. The set $\Omega_{i}$ can a finite set of actions, an interval, a sequence, etc. $\endgroup$
    – dgadjov
    Commented Oct 1, 2020 at 0:01
  • $\begingroup$ thanks @AsAnExerciseProve I'm aware of the fact that the action set for agents can be finite or for example an interval. My question was whether these can happen in the same game. I mean while an agent is choosing from a set of finite choices, the other choose from an interval. Ultimately, I am looking for convergence results in such games. Do you know any references? $\endgroup$
    – Has
    Commented Oct 2, 2020 at 0:52

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