If I have a sequential game, i.e. in each node (that I will call $t$) only one player choose an strategy from a finite space of strategies, Is it true there always exist a subgame perfect equilibrium in pure strategies? My intuition says me "yes", because at node $t$ a player could take the strategies from $t+1$ as given, and order all the available options where at least one would be the best (may be not unique, of course). If what I say it is true, I would very grateful to know who makes the proof or where to find it.
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1$\begingroup$ You have asked a very similar question before. 1. There is not enough information given. (Finite, infinite?) 2. In either case this looks like a homework/self study question with no effort shown. $\endgroup$– GiskardCommented Aug 24, 2017 at 18:10
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1$\begingroup$ If you understand what a sub-game perfect equillibrium is the answer is very intuitive. Following what Denesp says, if you provide some effort into answering the question I'd be glad to assist if you get stuck. $\endgroup$– Lee SinCommented Aug 24, 2017 at 18:12
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$\begingroup$ On a topic other than this question: I see that you ask a lot on math.SE and get a lot of answers. Consider ACCEPTING the answers by clicking the green check mark on the left of the answer. $\endgroup$– GiskardCommented Aug 24, 2017 at 18:46
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$\begingroup$ Sorry Denesp, the strategy space I was thinking is finite. This is only personal study and that's why maybe I'm ambiguous with my ideas. With respecto to the other topic, I didn't know that can do it, I will do it now, Thanks! $\endgroup$– hllspwnCommented Aug 25, 2017 at 18:35
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