<blockquote>
<p>Is it somehow suggesting that history does not matter?</p>
</blockquote>
<p>It is suggesting that history <em>may</em> not matter. They are just saying that if, in a given round <span class="math-container">$t$</span>, all players are willing to take the preceeding payoffs but otherwise forget what happened before, then the repated game starting in round <span class="math-container">$t$</span> is identical to the game starting in round <span class="math-container">$0$</span>, except for the now fixed payoffs earned before round <span class="math-container">$t$</span>.</p>
<p>The game and the strategies you can follow are identical, even if you chose not to follow some strategy in it because of something that happened before round <span class="math-container">$t$</span>, meaning you had a history dependent strategy. You also had the option not to follow this strategy in round <span class="math-container">$0$</span>, whether you did or did not do so is not relevant.</p>

CC BY-SA 4.0
2024-07-10T16:55:40.100Z
Thanks, can you take a look also at my other question https://economics.stackexchange.com/questions/58775/definition-of-stationary-subgame-perfect-nash-equilibrium-in-a-repeated-game
Star
CC BY-SA 4.0
2024-07-12T04:09:34.493Z
Unfortunately I am not familiar with the concepts you talk about it in that one.
Giskard
CC BY-SA 4.0
2024-07-10T16:34:26.117Z
2024-07-10T16:34:26.117Z
Giskard
<p>I am reading Mailath and Samuelson (2006), and I struggle to understand the sentence they have at p.191 on infinitely-repeated games: &quot;<em>Repeated games have the additional property that every history gives rise to an
identical continuation game.</em>&quot;</p>
<p>Can you explain to me what this means? Is it somehow suggesting that history does not matter? I confuse this with the fact that strategies are history-dependent.</p>

CC BY-SA 4.0
2024-07-10T16:29:19.227Z
This only seems to be true for infinitely repeated games, so perhaps add this context.
Giskard
<game-theory><repeated-games>
"Repeated games have the additional property that every history gives rise to an identical continuation game."
Star
# "Repeated games have the additional property that every history gives rise to an identical continuation game."

(Asked by: username_0 on 2024-07-10)

I am reading Mailath and Samuelson (2006), and I struggle to understand the sentence they have at p.191 on infinitely-repeated games: "*Repeated games have the additional property that every history gives rise to an
identical continuation game.*"

Can you explain to me what this means? Is it somehow suggesting that history does not matter? I confuse this with the fact that strategies are history-dependent.

**Tags:** game-theory, repeated-games
> **Comments:**
> **username_1**: This only seems to be true for infinitely repeated games, so perhaps add this context.  

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## 1 answers

### Answer by username_1 on 2024-07-10. Score: 1 | Accepted answer

> Is it somehow suggesting that history does not matter?

It is suggesting that history *may* not matter. They are just saying that if, in a given round $t$, all players are willing to take the preceeding payoffs but otherwise forget what happened before, then the repated game starting in round $t$ is identical to the game starting in round $0$, except for the now fixed payoffs earned before round $t$.

The game and the strategies you can follow are identical, even if you chose not to follow some strategy in it because of something that happened before round $t$, meaning you had a history dependent strategy. You also had the option not to follow this strategy in round $0$, whether you did or did not do so is not relevant.

> **Comments:**
> **username_0**: Thanks, can you take a look also at my other question https://economics.stackexchange.com/questions/58775/definition-of-stationary-subgame-perfect-nash-equilibrium-in-a-repeated-game  
> **username_1**: Unfortunately I am not familiar with the concepts you talk about it in that one.  

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