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how to screen off evolutionary game theory: which problems are solvable and which are not?

In Uncategorized on April 22, 2010 by wenwenfan

I had this question since Lynn asked about the Odd Man Out game in the seminar. I talked to Sheng about it, and we had some tentative answers, but I don’t know what other people think. I would like to hear from you about it.

In Yasha’s paper, he realized a problem for the Odd Man out game to model coalitions: the game predicts a much higher frequency of the break-up of coalitions. This problem can be interpreted in two ways: either it does not fulfill the empirical criterion (because its prediction is disconfirmed by emprical data) or there is some feature the game should incorporate. Yasha takes the second interpretation. This case seems the way Zac does in his paper about the Prisoner’s Dimma game. Zac found out that the Prisoner’s Dilemma game cannot yield a prediction of altruistic behavior, so he identified two features (namely, iteration and correlation) that should be incorporated into the game. As long as those features are considered, the game can yield a good prediction.

My question is: how do we know when the model simply fails to meet the empirical criterion and when it neglects some essential features it should consider? Sheng and I thought that perhaps we need some standard to judge when the empirical criterion is met and when it’s not. It may also boil down to the question what features a game should represent what it should not.

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3 Responses to “how to screen off evolutionary game theory: which problems are solvable and which are not?”

  1. That was exactly my question in class. Couldn’t have put it better!
    My conclusion that day to myself was that we could have a post hoc or ad hoc criteria of whether it is the model’s fault or the contingent features of the empirical case’s fault that the prediction does not hold.

    The post hoc criteria would be, *only when* prediction fails do we need to seek if the empirical case has features that are causing the prediction to fail. In the coalition shift rate case, it is the presence of a linear dominance hierarchy that provides the alpha male an additional incentive to break up coalitions. This is not predicted by the odd man out game.

    The ad hoc criteria would be to to explicitly lay out exactly what aspect of the empirical case does the model aim to explain. In this case, it is the incentive to form resource-dividing coalitions under strong incentives, in this case, the incentive is to become the alpha male.

    Combining the two, the odd man out game successfully models this aspect of the society, but it does not aim to model the rate of coalition shift. So the odd man out game can be viewed as an idealized model with idealizing assumptions. These assumptions can only take you so far. One needs to recognize how far it can take (ad hoc criteria). Once you get there and find that there are additional problems, you then look into the model and discover what assumptions need to be altered to account for the additional issues (post hoc criteria).

    This satisfied me for the day. What do you think?

  2. Hi Wenwen and Lynn. Good question. (I did not realize that this was your question Lynn, sorry). I admit, I did not give a very precise account of the empirical criterion, which is why André justifiably hammered me so hard in class. The empirical criterion is about prediction. You don’t want your model to be making predictions that are factually incorrect. So, like I said, The Stag Hunt predicts that coalitions are stable and the Prisoner’s Dilemma predicts that you can benefit by defecting on your partner in the first iteration. Both make predictions that aren’t seen in nature.

    But the Odd Man Out game predicts rapidly fluctuating coalitions, so why not abandon this model as well? The idea is that not all model breakdowns are the same. (It is important to remember here that the Odd Man Out game meets the other criterion.) Sometimes when your model breaks, it can be informative. And I think in the case of coalitional behavior the Odd Man Out game’s breakdown is minor enough to be acceptable and at the same time informative. So why is the bad prediction about the rate of change acceptable and informative when it comes to model decision and the prediction that coalitions are stable not? The idea is that the instability of coalitions is still captured on the Odd Man Out game; hence an essential feature is captured. The breakdown is only a matter of “degree”—how rapidly will they fluctuate. The Stag Hunt can’t capture the essential feature, so the breakdown is more serious. What features you need your model to capture will depend on the questions you are asking and the behavior that you are trying to model. Since the behavior in question is coalitional behavior, the model needs to address both formation and maintenance, and since instability is part of maintenance, given what we know about chimpanzee societies, the Odd Man Out game is a better model of the behavior.

    That part of the paper got me thinking about model breakdown. And as I noted, sometimes model breakdowns suggest scraping the model, sometimes they can be informative. When in general is it the case that these breakdowns are informative and acceptable? I think that is a very interesting question, but a project for the future, since my paper is only trying to make the methodological point that that three-person games are indeed important to the explanatory project of explaining the evolution of prosocial behavior where two-person games have been the norm.

  3. Lynn,

    I like your post hoc criteria. This criteria can help us to see whether there is any feature that can be taken by the model to explain/predict the target phenomenon.

    As for the ad hoc criteria, I am unsure how much it helps. The reason is that even the prinsoner’s dilemma game can be interpreted as failing to model altruistic behaviors. In this case, we might say that the prisoner’s dilemma game fails to fulfill the ad hoc criteria. But we know that this problem can be fixed by taking in iteration and correlation. So, I think the post hoc criteria is a terrific idea, but the ad hoc criteria either does not help or isn’t essential.

    Yasha,
    I agree with what you said. The way the Odd Man Out game breaks down is different from the way the Stag Hunt game breaks down. We may say that the former is a problem in quantity while the latter is a problem in quality (as you suggest the essence/degree difference).

    This reply sufficies for the behavior of coalitions, but it doesn’t suffice for altruistic behaviors, for Zac shows that without iteration and correlation, the Prinsoner’s Dilemma Game doesn’t predict altruistic behaviors. And that is a problem in essence, or quality. (I know that Sober uses the Prisoner’s Dilemma Game without appealing to iteration and correlation, but I am skeptical whether using the average payoff is legitimate. I may be wrong, but I am inclined to think that sometimes we can’t even make the prediction we want without taking in any additional features.)

    So coming back to the behavior of coalitions, I accept your explanation of the breakdown of the Odd Man Game Out game. I am just skeptical of the explanation in general.

    Another thing I want to call to your attention: in your paper, you show that the Prionser’s Dilemma Game and the Stag Hunt Game fail to fulfill both criteria you propose. On the other hand, the Odd Mand Out game fulfills both criteria. I wonder whether a game will always fulfill or fail in both respects. If so, it may show that the two criteria are not independent of each other. And in that case, the formulation of the criteria needs revision.

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