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Quick question on Zach’s Paper

In Uncategorized on April 19, 2010 by Leo

Since I think we’ll be talking mostly about Yasha’s paper tomorrow, here’s a quick question I had on Zach’s paper:

Zach’s paper distinguishes between two game-theoretic approaches: the static approach and the dynamic approach. The static approach focuses on characteristics of the strategy itself. The dynamic approach focuses on how players settle on a particular strategy. However, it is unclear to me whether or not these are actually two distinct approaches. Is it not the case that the dynamic approach merely specifies which of the equilibria already picked out by the static approach that players will actually converge on? That is, does the dynamic approach actually subsume the static approach, by first identifying all the possible equilibria, and then improve upon it by identifying a subset of those equilibria which will end up being chosen by the players given certain initial conditions?

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I think that in relatively simple games like Hi-Lo, that’s a good way to look at it. Remember that the homework Zac assigned was a series of Hi-Lo games that usually produced three equilibria (two pure and one mixed), but there was no explanation for why a group would prefer one equilibrium over the other. The dynamic approach provides that explanation. The pure Hi strategy is fitter than the other strategies, especially given a high degree of correlation.

But, I don’t think that this necessarily holds. I seem to recall something in Zac’s seminar about how, given a sufficiently complex game or set of starting conditions, players will never converge on a strategy. Rather, they will cycle through available strategies as they become more or less advantageous over time.

This leads me to think that static and dynamic game theory are explaining two different things. I don’t think you can have dynamic without static, but if I only want to explain one-shot games or what my options are, I can do so by only using static games. Dynamic games seem more appropriate for ex post facto questions like, “Why was strategy x chosen when x, y, and z were all available options?”

Hi Leo. I concur with Jake’s nice response to your question. Another way to think about the differences between the two approaches is that the dynamic approach gives us a “how possibly” explanation. A further question is what the value of this how possibly explanation is, especially since it is based on chosen parameters. One way that Randy suggested to me was that you can give your how possibly explanation more oomph by running it with many different parameters and seeing if you get the same result. If so, then your result will be robust and perhaps have more oomph.

Leo,

Both Jake’s and Yasha’s response are helpful. You are certainly right that the dynamic approach cannot work without the notion of equilibrium, but the dynamic approach does not focus on the state of equilibrium, but how equilibrium is reached.

I offer another way to think of this matter. The dynamic/static approach distinction is just the procedure/state distinction. In ethics, people like to distinguish procedural justice and substantive justice, where the former is roughly the fairness of the process or procedure and the latter is roughly the fairness of the situation or state. We may say that procedural justice aims at substantive justice, but this is not the focus of it. Procedural justice is more about how to make the process fair to everyone involved than about whether the situtaion everyone ends up with is fair.

We may understand the dynamic/static approach distinction in the same way.