Tit for Tat is widely acknowledged as being the most successful strategy in game theory, that this is true is important since it directly affects big things - like foreign policy.
It seem clear that human beings have a capacity to harbour grudges over generations, and that these grudges tend to stem from retribution being aimed at the wrong person, or an innocent person who is a member of a perceived group through no choice of his or her own. This creates positive feedback, such that any person who has been a victim of mis-applied retribution is likely to feel injustice and seek revenge, which can also be mis-applied ad infinitum.
Tit for Tat models that I have seen imply perfect information flow, whereas the real world case of in-group/out-group mentality and grudges could be simply modelled by adding noise to the system.
I believe it would be simple to model this and to test whether it has any impact on the assumption that Tit for Tat is universally successful.
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A very simple game theory model is based upon a game where two subjects are told some rules of co-operation and play multiple rounds of a game where there is a proportional reward for their choice to either Defect or Co-operate during each round.
This game can be seen at the 10th minute of the Documentary ‘Nice Guys Finish First’, here.
The rewards are based upon a points system: 3 points each for mutual co-operation, 2 points each for mutual defection and 4 points for the defector and one for the co-operator, where they don’t mutually agree to co-operate or defect.
This points system implies a benefit for the system as a whole, for mutual co-operation. (i.e. 6 points total vs. 5 or 4 for defections).
Matrix for two player (defect, co-operate)
– C — D –
C 3/3 1/4
D 4/1 2/2
This situation tends to lead to a Tit for Tat strategy for 2 players, over multiple rounds.
[Interestingly, it could be tied to the work expended in gaining a reward (energy burned to hunt vas energy gained from meat etc.) to create a thermodynamic model, and more generally an information theory model.]
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Experiment one
Introduce noise into the system with the intention of modeling real world situations where information flow is rarely perfect.
Extend the original game to include ‘noise’, i.e. where player A or B are given the reward as if their choices had been different, but still consistent with the rules governing their own choice (i.e. if they can’t see the other players rewards, it is impossible to tell that there is any ‘noise’ in the system.). For example choosing to mutually co-operate means that instead of being a 3 points each player game, it is either a 1 point/3 point (player A imagines this as 1 point/ 4 point) or 3 point 3 point game.
Plot the players strategies relative to different values between 0 and 1 for the noise probability, to see if there are any ‘phase changes’.
Experiment two
introduce a third player, where the noise, instead of being a background noise is noise from another player. i.e. sometimes the rewards/punishment are given to the wrong people via swapping. This is intended to mimick the real world situation where stereo-typing means that defection from one person is imagined to come from another leading to a grudge which when applied creates a feeling of injustice, and therefore incentive for retribution.
Setup:
3 players, each player plays the other two simultaneously.
The number of points that an oponent gets must be hidden (i.e. you can imply from your reward, what the other player has done).
A fuzzyness variable can be set to make a random number of games (a game is a single co-operate/defect choice) have their ‘circuit switched’, i.e. as player A, your reward for game A/B is actually based on game A/C without you knowing it.
My hunch is that you need to introduce a degree of altruism (i.e. co-operating after your opponent defects) to compensate for mistaken communication, and that the value of this altruism variable is non-linear.
Perhaps there is a critical upper and lower threshold where its effectiveness works, this being the range of values where tit for tat can be restored through forgiving, altruistic behaviour.
If an online poll based upon the experiments above were created, it could be tested.
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