<p>Like the extensive form of every simultaneous move game, the extensive form of the Prisoner's Dilemma (PD) has no proper subgames. Its only subgame is the game itself.</p>
<p>However, your argument that &quot;the game ... has no information sets&quot; is not correct. In the extensive form of the PD, player 1 has a unique decision node, and the singleton set containing this node is his unique information set. Player 2 has 2 decision nodes, both belonging to her unique information set. So there are 2 information sets in the extensive form of the PD.</p>
<p>It's not clear what you mean with a &quot;main&quot; decision node. The game has a total of 3 decision nodes, but only the root corresponds to a singleton information set. That's also the reason for the absence of proper subgames.</p>

CC BY-SA 4.0
2023-04-27T13:41:03.423Z
2023-04-27T14:33:52.043Z
2023-04-27T14:33:52.043Z
VARulle
<p>In the most basic form of a prisoner's dilemma game [2x2; Cooperate or Defect, imperfect information], how many total subgames are present?</p>
<p>Preparing for an exam and this solution is not available. My answer would be that there is one subgame. I would argue this as the solution because the game has imperfect information, and therefore has no information sets. Since the game is also one-shot and simultaneous move, therefore only have one main decision node (since the players cannot see one another's choices).</p>
<p>If this is incorrect, please feel free to assist. Thank you.</p>

CC BY-SA 4.0
2023-04-27T13:37:52.190Z
Why should it have incomplete information? Do you mean *imperfect* information?
VARulle
<game-theory>
Total Number of Subgames in a Standard Prisoner's Dilemma
lime
# Total Number of Subgames in a Standard Prisoner's Dilemma

(Asked by: username_0 on 2023-04-27)

In the most basic form of a prisoner's dilemma game [2x2; Cooperate or Defect, imperfect information], how many total subgames are present?

Preparing for an exam and this solution is not available. My answer would be that there is one subgame. I would argue this as the solution because the game has imperfect information, and therefore has no information sets. Since the game is also one-shot and simultaneous move, therefore only have one main decision node (since the players cannot see one another's choices).

If this is incorrect, please feel free to assist. Thank you.

**Tags:** game-theory
> **Comments:**
> **username_1**: Why should it have incomplete information? Do you mean *imperfect* information?  

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## 1 answers

### Answer by username_1 on 2023-04-27. Score: 3

Like the extensive form of every simultaneous move game, the extensive form of the Prisoner's Dilemma (PD) has no proper subgames. Its only subgame is the game itself.

However, your argument that "the game ... has no information sets" is not correct. In the extensive form of the PD, player 1 has a unique decision node, and the singleton set containing this node is his unique information set. Player 2 has 2 decision nodes, both belonging to her unique information set. So there are 2 information sets in the extensive form of the PD.

It's not clear what you mean with a "main" decision node. The game has a total of 3 decision nodes, but only the root corresponds to a singleton information set. That's also the reason for the absence of proper subgames.


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