In one episode of Golden Balls, a player named Nick successfully meta-games the game by transforming it from the Prisoner’s Dilemma (where defection is rational) to the Ultimatum Game (where cooperation is rational)
One sentence, three false claims about game theory.
The game did not begin as a Prisoner’s Dilemma. The only thing that determines a Prisoner’s Dilemma is the payoffs of the game and Golden Balls simply doesn’t have the payoffs that the Prisoner’s Dilemma has and so isn’t one.
If you don’t use scare quotes around “rational” when you claim that irrational things are rational then you are wrong. Mind you, this isn’t a Prisoner’s Dilemma and the reason that defection is always “rational” (as claimed by CDT) in the Prisoner’s Dilemma is that defecting gives better payoffs than cooperating when the other defects (or cooperates). This doesn’t apply in golden balls. The reasoning is different and far less straightforward. That makes this error rather moot.
Nick didn’t convert the problem into an Ultimatum Game. He converted it from Golden Balls before he uttered a few arbitrary verbal symbols to Golden Balls after he uttered a few verbal symbols. The game theoretic meaning of those words is nothing, they are no signal whatsoever. We can see this in that he in fact is lying about his choice and chooses split. This wouldn’t be an ultimatum game even if the decisions were not simultaneous. In this case they are simultaneous—Nick chooses his ball at the end, just like Ibrahim and so even uses future tense when describing what he will do. Ibrahim could just as credibly say “I’m going to chose steal unless I believe you will chose split” and his words carry the same (negligible) weight.
A sequence which teaches those new to game theory to make exactly the kind of annoying mistakes that those new to game theory typically make is worse than no sequence at all.
As far as I know, this version is a form of prisoner’s dilemma: Payoff(C,D) ≤ Payoff(D,D) < Payoff(C,C) < Payoff(D,C). Normally, Payoff(D,D) is > (strictly greater than) Payoff(C,D), not just (equal or greater than), but it’s still reasonable to call this game a weak form of prisoner’s dilemma, as they share most characteristics.
Nothing to say here, but I apparently have to put a “2.” in if I want the “3.” from below to be represented properly.
Technically you’re right, though in this world of evolution and repeated social interaction, Nick did change the game by gambling not alone with money, but with his trustworthiness as a benevolent human being as well. Nick would look like a total douche to most people who get to know what he was doing, including his friends and family, if he chose steal and took the money all for himself. By making the air pressure oscillate in a certain way, Nick made it long-term unfavourable for him to steal the money completely, so the best he could do from there on was probably to either split or to steal and then split. From this perspective, he in fact did change the payoff function.
The specific problem with calling the last game a “prisoner’s dilemma” is that someone learning about game theory from this article may well remember from it, “there is a cool way to coordinate on the prisoner’s dilemma using coin flips based on correlated equilibria” then be seriously confused at some later point.
Of course, by changing the payoff matrix, Nick also changed the game, so after him putting in some more of his stakes, it wasn’t Golden Balls / PD anymore but a game which had the structure Nick favoured. What is to be learned from this article is how to design games to your own profit—whether you are watching from the outside or playing from the inside.
Apparently I didn’t quite understand what you wanted to tell me—I’m sorry! Yes, as an introduction to game theory, this indeed is a problem. Example #6 is a bit out of place for that, as game theory here didn’t work in practice in the sense that it didn’t make accurate predictions.
Technically you’re right, though in this world of evolution and repeated social interaction
In “this world of repeated social interaction” nothing is a True Prisoner’s Dilemma. Or a true One Shot Ultimatum Game or one shot game of any kind. This post is about bloodthirsty pirates offering only some of their minions $20 out of $17,000, others $0 and he is still confident that they will not overthrow him despite actively wanting him dead. The “oh, but reputation effects” objection is absurdly out of place.
Then I have to raise the question why one should bother to discuss models that don’t reflect reality well enough to make accurate predictions, in this case a real-world example.
The post consists of 6 examples. The first three are pure theory and wouldn’t stand a chance in practice. It’s however insightful to think about them to realize how powerful the designer of a game, in theory, can be.
The fourth example is a game that has been tried in practice, with apparently highly profitable results. Here, game-theory with a “rational actor model” delivers accurate predictions (that is, if every player is, in a Bayesian Game, confident enough that his opponent will eventually not bet more money, one SPE is to always invest more, correct me if I’m wrong). Thus, it’s in this case fine to apply game theory to the real world, as it works in most cases, under certain assumptions.
The fifth example, as you noted, stems from the realm of fiction and is useful for the pondering of game theory, but not useful in practice.
The last example is, like the fourth example, something that has actually happened. However, in this case, after Nick has uttered a few words that seem meaningless from a game theoretic point of view, game theory (with the payoff matrix for Golden Balls and the “rational actor model”) no longer makes accurate predictions. This means that perhaps, we should modify our model in order to get out a better prediction. One way to do so is to change the payoff matrix, another is to see the game as an instance of repeated PD. Also, one could choose to model the people with a rule-based or behavioural model—If my opponent has openly, in public, announced that he wants to split fairly if I do X, then I do X.
What’s left is that, while game theory is useful in modelling the real world at times, at times it is not. And when it is not, in my opinion one should accept this fact and use a different model.
Another note about “rational actor model” vs. “rule-based model” and “behavioural model”:
The rational actor model often applies in the real world if the stakes are high, the game is repeated several times, it’s a group decision and/or the coices to be made are fairly easy. It says that people have a goal and optimize for it. The objective can be money, but people are also allowed to have a different payoff function. It is, of course, not a model of rational people in the sense that these are always winning, more like academia-rational.
Behavioural models attempt to model people based on how they behaved before. These models take into account biases that we may have.
Rule-based models are based on simple rules that agents follow. These are often easy to write down, but can be exploited.
One sentence, three false claims about game theory.
The game did not begin as a Prisoner’s Dilemma. The only thing that determines a Prisoner’s Dilemma is the payoffs of the game and Golden Balls simply doesn’t have the payoffs that the Prisoner’s Dilemma has and so isn’t one.
If you don’t use scare quotes around “rational” when you claim that irrational things are rational then you are wrong. Mind you, this isn’t a Prisoner’s Dilemma and the reason that defection is always “rational” (as claimed by CDT) in the Prisoner’s Dilemma is that defecting gives better payoffs than cooperating when the other defects (or cooperates). This doesn’t apply in golden balls. The reasoning is different and far less straightforward. That makes this error rather moot.
Nick didn’t convert the problem into an Ultimatum Game. He converted it from Golden Balls before he uttered a few arbitrary verbal symbols to Golden Balls after he uttered a few verbal symbols. The game theoretic meaning of those words is nothing, they are no signal whatsoever. We can see this in that he in fact is lying about his choice and chooses split. This wouldn’t be an ultimatum game even if the decisions were not simultaneous. In this case they are simultaneous—Nick chooses his ball at the end, just like Ibrahim and so even uses future tense when describing what he will do. Ibrahim could just as credibly say “I’m going to chose steal unless I believe you will chose split” and his words carry the same (negligible) weight.
A sequence which teaches those new to game theory to make exactly the kind of annoying mistakes that those new to game theory typically make is worse than no sequence at all.
As far as I know, this version is a form of prisoner’s dilemma: Payoff(C,D) ≤ Payoff(D,D) < Payoff(C,C) < Payoff(D,C). Normally, Payoff(D,D) is > (strictly greater than) Payoff(C,D), not just (equal or greater than), but it’s still reasonable to call this game a weak form of prisoner’s dilemma, as they share most characteristics.
Nothing to say here, but I apparently have to put a “2.” in if I want the “3.” from below to be represented properly.
Technically you’re right, though in this world of evolution and repeated social interaction, Nick did change the game by gambling not alone with money, but with his trustworthiness as a benevolent human being as well. Nick would look like a total douche to most people who get to know what he was doing, including his friends and family, if he chose steal and took the money all for himself. By making the air pressure oscillate in a certain way, Nick made it long-term unfavourable for him to steal the money completely, so the best he could do from there on was probably to either split or to steal and then split. From this perspective, he in fact did change the payoff function.
The specific problem with calling the last game a “prisoner’s dilemma” is that someone learning about game theory from this article may well remember from it, “there is a cool way to coordinate on the prisoner’s dilemma using coin flips based on correlated equilibria” then be seriously confused at some later point.
Of course, by changing the payoff matrix, Nick also changed the game, so after him putting in some more of his stakes, it wasn’t Golden Balls / PD anymore but a game which had the structure Nick favoured. What is to be learned from this article is how to design games to your own profit—whether you are watching from the outside or playing from the inside.
Apparently I didn’t quite understand what you wanted to tell me—I’m sorry! Yes, as an introduction to game theory, this indeed is a problem. Example #6 is a bit out of place for that, as game theory here didn’t work in practice in the sense that it didn’t make accurate predictions.
In “this world of repeated social interaction” nothing is a True Prisoner’s Dilemma. Or a true One Shot Ultimatum Game or one shot game of any kind. This post is about bloodthirsty pirates offering only some of their minions $20 out of $17,000, others $0 and he is still confident that they will not overthrow him despite actively wanting him dead. The “oh, but reputation effects” objection is absurdly out of place.
Then I have to raise the question why one should bother to discuss models that don’t reflect reality well enough to make accurate predictions, in this case a real-world example.
The post consists of 6 examples. The first three are pure theory and wouldn’t stand a chance in practice. It’s however insightful to think about them to realize how powerful the designer of a game, in theory, can be.
The fourth example is a game that has been tried in practice, with apparently highly profitable results. Here, game-theory with a “rational actor model” delivers accurate predictions (that is, if every player is, in a Bayesian Game, confident enough that his opponent will eventually not bet more money, one SPE is to always invest more, correct me if I’m wrong). Thus, it’s in this case fine to apply game theory to the real world, as it works in most cases, under certain assumptions.
The fifth example, as you noted, stems from the realm of fiction and is useful for the pondering of game theory, but not useful in practice.
The last example is, like the fourth example, something that has actually happened. However, in this case, after Nick has uttered a few words that seem meaningless from a game theoretic point of view, game theory (with the payoff matrix for Golden Balls and the “rational actor model”) no longer makes accurate predictions. This means that perhaps, we should modify our model in order to get out a better prediction. One way to do so is to change the payoff matrix, another is to see the game as an instance of repeated PD. Also, one could choose to model the people with a rule-based or behavioural model—If my opponent has openly, in public, announced that he wants to split fairly if I do X, then I do X.
What’s left is that, while game theory is useful in modelling the real world at times, at times it is not. And when it is not, in my opinion one should accept this fact and use a different model.
Another note about “rational actor model” vs. “rule-based model” and “behavioural model”:
The rational actor model often applies in the real world if the stakes are high, the game is repeated several times, it’s a group decision and/or the coices to be made are fairly easy. It says that people have a goal and optimize for it. The objective can be money, but people are also allowed to have a different payoff function. It is, of course, not a model of rational people in the sense that these are always winning, more like academia-rational.
Behavioural models attempt to model people based on how they behaved before. These models take into account biases that we may have.
Rule-based models are based on simple rules that agents follow. These are often easy to write down, but can be exploited.