I didn't read the article but I assume the ultimatum consists of "I'll cooperate x% of the time if you cooperate 100% of the time. Otherise I'll defect 100%".
Normally in game theory, such statements are not seen as "credible", i.e. you assume the other person is bluffing and you go on to defect 100% of the time.
Prisoner's Dilemma is about cooperation. "How much do you trust this person"
Ultimatum Game is about bargaining. "At what point are you willing to pay to punish someone for an unfair deal?"
Still processing the paper, but the implication here would be that you can link the two models, but the payoff to doing so critically depends on how much the dominant player is capable of modeling the other player's mind.
It's evolutionarily favourable to accept the ultimatum. They claim that if you have theory of the other players mind you should reject the ultimatum and hope the other player gives you a better deal. Giving you a better deal isn't possible in the original ultimatum game, but this is more of an iterated ultimatum game.
Reality is complex, so we use simplified models in theories. But then the results from the models don't generalize back to reality very well. I think the tradeoffs are well known, and I don't think there's any magical solution.
It's simple and demonstrates that the Nash equilibria of a game can deviate from the strategies that produce the best payoff. I think most pop sci corollaries people try to draw from it are overreaches at best.
I would agree that Prisoner's Dilemma is an exceptional case, except that it can be used.
Someone in a position of power may choose to set up a prisoner's dilemma - let's say, between you and your colleagues - to disadvantage you both, while giving an illusion of choice.
A big reason for cooperating in iterated prisoners dilemma in nature is that the benefits from cooperating with relatives is huge.
And in a pool of cooperative agents doing some "last-turn-defect" strategy while theoretically better than cooperate-always, is complicated with small payoff.
Covered in some detail in Robert Axelrod's "Evolution of Cooperation" from 1984 [0] which is a book resulting from the original paper with W D Hamilton. Anatol Rappaport submitted "Tit for tat" as a strategy in a computerised tournament of programs adressing the Prisoners Dilemma, , and it wiped the floor with the opposition. I don't recall the full details, there was a second round with some restrictions, Rappaport simply submitted TfT again and it came out well even with constraints on it.
There is actually a better strategy than tit for tat, for iterated prisoner's dilemma played in a tournament setting where the winner is determined by total score at the end of all rounds.
The strategy is to submit lots of entrants to the tournament rather than just one, then play tit for tat against all opponents except those that are in the clique. The clique players then lose on purpose to a specifically-chosen player, maximizing that players score.
If you don't want to do it this way and instead care about maximizing the total scores of the clique as a whole, you can default to every clique member always cooperating.
Even in cases where the opponent is "blind", you can use a special pattern of bets to signal that the other player is a member of the clique and then play your win-maximizing strategy once the signal is detected.
This kind of thing has real-world implications. For example: imagine a poker game with ten players, all of the same skill level and without a rake. Nine of the players can collude (say, show each other their hidden cards and make decisions based on the shared information), making it significantly less likely than a 10% chance that the targeted player will win. I suspect this is already done to an extent in extremely high-stakes games (say, $1MM+).
At lease for standard iterated prisoners dilemma AI tournaments, this strategy was completely legal - I read about it severals years ago when it was first used to win a prominent one.
The poker one already happens in real life all the time - if friends go to play at the same table, they often play differently than with a stranger.
I don't recall where or when I read it, but there is a strategy that usually beats Tit-fot-tat.
Tit for tat, but also a small (random) chance of forgiving (giving a break) anyway. I believe the reason that won is that this allowed for recovery in the face of understandings and as long as the chance wasn't that large the cost also wasn't.
There is a great lecture from Robert Sapolsky/Stanford [2010] about behavioral evolution / prisoner's dilemma / tit for tat strategy: https://youtu.be/Y0Oa4Lp5fLE
Should be: "Iterated Prisoners Dilemma Contains Strategies That Dominate Any Evolutionary Opponent at a Game as Simple as the Prisoner's Dilemma"
You can write a perfect tic-tac-toe program with relatively simple rules, but an evolutionary strategy will wipe the floor at Go. This kind of modelling has value but real life is incredibly complicated, complicated strategies destroy simple ones as the rules of the game become more complex. Our brains are extremely expensive organs, and they're built that way for a reason. I think people are way trigger-happy extrapolating models like this to the real world.
Both are problems. Our brains have a tremendous amount of compute and use complex, nuanced, adaptive strategies.
The clearest example is how much energy we spend modelling other humans' thought processes. We spend so much because a simple permutation of tit-for-tat isn't sufficient - it will lose. It's an arms race to use complex strategies, an outcome which is specifically precluded in the model. I'd argue the fact observable reality is so divergent from the model means we should be skeptical of the applicability of the model.
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[ 2.2 ms ] story [ 74.4 ms ] threadInteresting, if true, would the fist linkage between the Prisoner's Dilemma and the Utlimatum Game.
https://en.wikipedia.org/wiki/Ultimatum_game
Normally in game theory, such statements are not seen as "credible", i.e. you assume the other person is bluffing and you go on to defect 100% of the time.
Ultimatum Game is about bargaining. "At what point are you willing to pay to punish someone for an unfair deal?"
Still processing the paper, but the implication here would be that you can link the two models, but the payoff to doing so critically depends on how much the dominant player is capable of modeling the other player's mind.
Aka smartest model/strategy/robot/person wins.
In most real world situations, the payoffs are much different than the PD ones.
Collaborate, and you may lose or win a little. Defect and for most cases, your payoff is 0.
Someone in a position of power may choose to set up a prisoner's dilemma - let's say, between you and your colleagues - to disadvantage you both, while giving an illusion of choice.
And in a pool of cooperative agents doing some "last-turn-defect" strategy while theoretically better than cooperate-always, is complicated with small payoff.
*Wherein the player does whatever their opponent did in the previous round.
[0] https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation
The strategy is to submit lots of entrants to the tournament rather than just one, then play tit for tat against all opponents except those that are in the clique. The clique players then lose on purpose to a specifically-chosen player, maximizing that players score.
If you don't want to do it this way and instead care about maximizing the total scores of the clique as a whole, you can default to every clique member always cooperating.
Even in cases where the opponent is "blind", you can use a special pattern of bets to signal that the other player is a member of the clique and then play your win-maximizing strategy once the signal is detected.
This kind of thing has real-world implications. For example: imagine a poker game with ten players, all of the same skill level and without a rake. Nine of the players can collude (say, show each other their hidden cards and make decisions based on the shared information), making it significantly less likely than a 10% chance that the targeted player will win. I suspect this is already done to an extent in extremely high-stakes games (say, $1MM+).
The poker one already happens in real life all the time - if friends go to play at the same table, they often play differently than with a stranger.
Forgiving: always give, even to those who don't cooperate
Tit-for-tat: cooperates by default but does not reward defectors/freeloaders. This often the best strategy.
Interesting how this applies to software licenses.
Permissive licenses are clearly forgiving actors.
Copyleft/protective licenses are a gentler version of tit-for-tat.
Tit for tat, but also a small (random) chance of forgiving (giving a break) anyway. I believe the reason that won is that this allowed for recovery in the face of understandings and as long as the chance wasn't that large the cost also wasn't.
You can write a perfect tic-tac-toe program with relatively simple rules, but an evolutionary strategy will wipe the floor at Go. This kind of modelling has value but real life is incredibly complicated, complicated strategies destroy simple ones as the rules of the game become more complex. Our brains are extremely expensive organs, and they're built that way for a reason. I think people are way trigger-happy extrapolating models like this to the real world.
The clearest example is how much energy we spend modelling other humans' thought processes. We spend so much because a simple permutation of tit-for-tat isn't sufficient - it will lose. It's an arms race to use complex strategies, an outcome which is specifically precluded in the model. I'd argue the fact observable reality is so divergent from the model means we should be skeptical of the applicability of the model.
See eg. https://www.nature.com/news/physicists-suggest-selfishness-c... which describes that political struggle going on for the last 40 years. This was eg countered by https://www.researchgate.net/publication/236189156_The_Evolu...