<p>In my game theory class we recently learned about dynamic games and I wanted to know whether I solved my homework problem correctly (and how to attempt the second part).</p>
<p><a href="https://i.sstatic.net/whRgw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/whRgw.png" alt="Game tree" /></a></p>
<p>a)  Determine all strategies of players 1,2,3.</p>
<p>b)  Determine the subgame perfect equilibria/equilibrium of the game.</p>
<p>For a) I found the following strategies: Player 1 can play strategy A or B, player 2 can play CE, CF, DE, DF, player 3 can play GI, GJ, HI, HJ. Would that be correct?</p>
<p>Unfortunately, I don’t even know how to tackle problem b). I know that I should probably use backward induction, but I don’t know how exactly it would be applied here.</p>

CC BY-SA 4.0
2023-11-15T10:49:41.947Z
Hi! It is not clear exactly what you are having difficulties with. Have you tried looking up what 'backward induction' is? Also, since you have determined the strategies, have you tried to find the general Nash-equilibria? (Do you know what a Nash-equilibrium is?)
Giskard
CC BY-SA 4.0
2023-11-15T12:59:36.270Z
Imagine you are player 3 and the course of play has reached your left decision node. You want to maximize your payoff. Would you choose $G$ or $H$? If you answer this question, you have already started applying backwards induction...
VARulle
<game-theory><dynamic-games><extensive-games>
Finding strategies and subgame perfect equilibria
l337n00b
# Finding strategies and subgame perfect equilibria

(Asked by: username_0 on 2023-11-15)

In my game theory class we recently learned about dynamic games and I wanted to know whether I solved my homework problem correctly (and how to attempt the second part).

[![Game tree](https://i.sstatic.net/whRgw.png)](https://i.sstatic.net/whRgw.png)

a) Determine all strategies of players 1,2,3.

b) Determine the subgame perfect equilibria/equilibrium of the game.

For a) I found the following strategies: Player 1 can play strategy A or B, player 2 can play CE, CF, DE, DF, player 3 can play GI, GJ, HI, HJ. Would that be correct?

Unfortunately, I don’t even know how to tackle problem b). I know that I should probably use backward induction, but I don’t know how exactly it would be applied here.

**Tags:** game-theory, dynamic-games, extensive-games
> **Comments:**
> **username_1**: Hi! It is not clear exactly what you are having difficulties with. Have you tried looking up what 'backward induction' is? Also, since you have determined the strategies, have you tried to find the general Nash-equilibria? (Do you know what a Nash-equilibrium is?)  
> **username_2**: Imagine you are player 3 and the course of play has reached your left decision node. You want to maximize your payoff. Would you choose $G$ or $H$? If you answer this question, you have already started applying backwards induction...  

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## 0 answers

