<p>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.</p>

CC BY-SA 3.0
2017-08-24T18:10:04.013Z
You have asked a [very similar question](https://economics.stackexchange.com/questions/15995/how-to-demonstrate-that-a-game-always-have-a-subgame-perfect-equilibrium-in-pure) 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.
Giskard
CC BY-SA 3.0
2017-08-24T18:12:29.143Z
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.
Lee Sin
CC BY-SA 3.0
2017-08-24T18:46:28.690Z
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.
Giskard
CC BY-SA 3.0
2017-08-25T18:35:17.950Z
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!
hllspwn
<game-theory><nash-equilibrium><dynamic-games>
Subgame Perfect Equilibrium with Pure Strategies in Sequential Games
hllspwn
# Subgame Perfect Equilibrium with Pure Strategies in Sequential Games

(Asked by: username_0 on 2017-08-24)

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.

**Tags:** game-theory, nash-equilibrium, dynamic-games

> **Comments:**
> **username_1**: You have asked a [very similar question](https://economics.stackexchange.com/questions/15995/how-to-demonstrate-that-a-game-always-have-a-subgame-perfect-equilibrium-in-pure) 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.  
> **username_2**: 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.  
> **username_1**: 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.  
> **username_0**: 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!  

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## 0 answers

