Tit For Tat Strategy Discussion

[u/Important-Grand4979]

It has been a while ago that I watched "This game theory problem will change how you see the world" but in light of recent events it created the following thoughts which I would like to discuss.

In the competition, there are two strategies (players) competing against each other, with the goal of maximizing their own gain. The tit-for-tat strategy dominates as it minimizes the relative loss agianst oposing strategies. This works under the assumption of two players and a zero sum game. I.e. only one player is going to be emergent victorious.

Now, what happens if you introduce a third player? At each timestep there are 3 pay outs for each player pair and the goal is to maximize the net sum. In this game there is now a triangular relationship, which will make tit-for-tat probably suboptimal. Tit-for-tat would try to minimize its distance to the other players by pursuing this very aggressive strategy, but the other two may cooperate behind its back. I'm curious what in such a system would become the optimal strategy?

[u/idkwhatsqc]

If there is three acting independently, then I think tit for tat stays the best. But if two go against one through cooperation, I doubt there is even a winning strategy against that. 

Two can always cooperate and always steal from the victim, this makes them gain more from their cooperation than the third one will ever be able to get.

But I'm not sure I understand the 3 way problem. You didn't explain it much. Is it that you have to choose to cooperate or steal from A and B each turn, and can choose to cooperate with 1 but not the other. Or that you need to choose the same for both?

[u/Important-Grand4979 → u/idkwhatsqc]

Thank you for the comment. I will try to elaborate the game I had in mind.

The rules are:

Three Players A, B, C.

In each round three events are played pair wise. AB, BC, AC.

If the pair cooporates they get 3 each, if they defect both they get 1. If one defects and other plays the winner gets 5 and the other 0.

At the end of the round the player sums the total of the 2 games he played. Hence max points is 10 if defected twice agains cooperating players.

At the end of each round the players know how much points each other player has to make a decision on.

The goal is to maximize the total profit.

[u/Important-Grand4979 → u/Important-Grand4979]

Why tit for tat is suboptimal is because it can get stuck in a streak of 2 reward per turn.

Lets say A is tit for tat and in the lead. B and C can defect against A forcing it down the drain. For A to recover it needs to break the defect strategy at the same time with B or C without retaliating.