# How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies?

If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to show that in every subgame a pure strategy it's a solution to the problem (maybe not unique) and then there is always a pure strategies equilibrium. But I'm not sure.

• I'm not sure the statement is true in general. The only SPE in matching pennies is in mixed strategies. Mar 29 '17 at 22:23
• Perhaps the OP has in mind finite extensive form games with perfect information, for which I believe the claim is true. Mar 30 '17 at 2:13
• This is true in mixed strategies, I think.
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Mar 30 '17 at 15:05
• I'm not saying that it's true for all games, sorry if I did not explain myself good. Its if I had an specific extensive game. Mar 31 '17 at 15:07
• Then you should tell us what this specific game is, and show that you've made some effort on trying to prove the result. Mar 31 '17 at 15:39