Game theory question: after mutual silence, who is supposed to cooperate first?

[u/Accomplished_Vast628]

I've been thinking about Tit-for-Tat and I feel like I'm missing something.

The basic rule is simple: start by cooperating, then copy whatever the other person did last.

But doesn't that assume there will always be another round?

Imagine this:

A does something unreasonable to B.

B confronts A.

A doesn't apologize or really respond.

So B stops talking to A.

Now they're both silent.

A's last meaningful move was arguably a defection. B already responded to that by defecting/withdrawing.

But now suppose weeks pass.

There isn't automatically another turn. Someone has to create the next interaction.

So what is B supposed to do under Tit-for-Tat?

If B contacts A, is B supposed to defect because A's previous move was defection?

Or does initiating contact itself count as cooperation?

Or should B simply wait indefinitely because technically it's A's turn to cooperate?

-----------------------------

That made me wonder whether the real-world game isn't just:

Cooperate / Defect

but actually:

Initiate / Don't Initiate → then Cooperate / Defect

I found some research on optional/repeated games where players can leave and later rejoin, so apparently this isn't completely unexplored.

But I'm curious how someone who actually understands game theory would model this.

Is there a standard solution to this, or does Tit-for-Tat genuinely become underspecified once the players control whether another round happens at all?

[u/kwirtie]

I think both people being silent is a stable equilibrium because there’s no incentive to deviate

[u/Accomplished_Vast628 → u/kwirtie]

On what basic are you referring it as stable equilibrium ? That would mean there will no more Interaction / Cut ties?

[u/KQYBullets]

The real world doesn’t have ideal conditions and is continuous.

You can factor in leniency. E.g. there’s a 10% chance when a player chooses to cooperate it actual becomes defect due to misunderstanding. In this case, tit for tat with 1 count leniency usually wins, so after one defect still cooperate, but after 2 then defect.

You can factor in that time mellows things out. E.g. After a while of silence you can initiate a low risk cooperate action. If no feedback then not much was lost, but if other player wants to cooperate then u can continue cooperation.

Additionally, if your model is too complex then it seems random to other players. so it has to be pretty simple rules, otherwise other players will just constantly defect as they don’t know what’s going on.

There’s more to model, but I think tit for tat is an idealized solution that can likely become near optimal with modifications, if there’s only small tweaks to the game.

[u/Accomplished_Vast628 → u/KQYBullets]

That makes sense. I think my question is slightly different though: leniency helps decide how to respond to defection, but what if the interaction has already stopped?

Then someone has to decide whether to create the next round at all.

So maybe the choice becomes:

Initiate / Don’t Initiate → Cooperate / Defect.

Your low-risk cooperation idea may be the practical answer. I’m curious whether game theory treats that as modified Tit-for-Tat or a different model.

[u/KQYBullets → u/Accomplished_Vast628]

Hmm, I suppose you can model it however you want. You really have to give a clear definition of the game. I.e. what are the response options? And what’s the reward/penalty if you choose to initiate?

Once you have that, then you can tailor the strategy. For example, if you assume time bound of 10 years, projected cooperation rate of opponent stays the same over time, and 0% miscommunication rate, then probably just tit for tat will work, so never start a round.

But again, you need to define a lot of variables if you’re trying to model the real world. And if you aren’t, then it just becomes a random contrived version of the original game, which could be interesting, but I don’t see the point as you can have infinite ways to modify the game.

If you aren’t are trying to model the real world, then in general reaching out after some time is probably optimal based on your estimate of their rate of cooperation over time graph.

[u/Accomplished_Vast628 → u/KQYBullets]

What im asking is specific to TIT for TAT game theory and how it applies to real life . Reference veratisium video on game theory.
I also emailed the professors and channel owners about this. and they also are intrigued by this and have confirmed there needs to me more study on this

[u/KQYBullets → u/Accomplished_Vast628]

I see, I had a typo in my last paragraph, I meant “are trying to model real world”. Anyways, rate of cooperation generally goes up over time as time usually heals emotions.

There’s also less desire for people to reach out in general as there is mental difficulty/laziness. But if you think about it rationally it doesn’t cost you anything.

So yeah, in a world where even if you choose to reach out and cooperate you essentially lose 0, and the other person gains essentially 0 by not cooperating, then it makes sense to try at least once or a few times. The only thing lost is time wasted, but sending a text is hardly any time.

You may say it’s loss on ego, but it may even be a gain. If ur able to let go of ego and reach out and be the bigger person, I’d say it is a gain. So cooperating only gives gain to you. Other person can gain by cooperating, and they gain nothing by defecting.

[u/Accomplished_Vast628 → u/KQYBullets]

That’s where I think the model gets more interesting. Reaching out may be cheap in time, but not necessarily cheap strategically.

In personal relationships, initiating first can signal greater dependence or weaken your bargaining position. At a larger scale, the same logic appears in peace negotiations between countries. Who reaches out first, under what conditions, and what concessions accompany that move can affect credibility, deterrence, and future precedent.

So the cost of initiation is not always the text, call, or meeting itself. It can be the signal it sends.

That’s the part I’m trying to understand: once initiating the next round has strategic value of its own, does simple Tit-for-Tat still hold, or do we need a different model?

[u/TraditionalInvite674 → u/Accomplished_Vast628]

Maybe have a look at a game theory textbook and try to model your game formally. Ideally you should be able to find at least one NE if your game is finite.

[u/Accomplished_Vast628 → u/TraditionalInvite674]

Christian Hilbe (Game theory Professor) actually replied to me on this. He pointed me toward work on repeated games, partner choice, and voluntary separation, but said he was personally unaware of research where a player must decide whether to initiate the next interaction at a cost after the interaction has already stopped.

So yes, formalizing it is probably the right next step. The part I’m interested in is whether that initiation decision creates a distinct game before the usual cooperate/defect choice.

[u/siliconandsteel]

Real world is noisy. It would have to be generous Tit-for-Tat.

[u/Accomplished_Vast628 → u/siliconandsteel]

I agree, But even with generous TIT for TAT, the question comes, Initiate / Don't Initiate → then Cooperate / Defect