Why economists should care about computational complexity When trying to convince economists of the relevance of complexity theory in print, is there a standard reference to cite? I am familiar with Noam Nisan's blog post, Tim Roughgarden's survey, and chapter 11 of Scott Aaronson's essay. These posts are accessible for computer scientists, but do not use the language of economists and are not published in venues typically read by them. Are there good arguments for the importance of the complexity of equilibiria, etc. targeted at economists? Is there a good historic overview of how economists have responded to pressure from computer scientists?
It could be argued that neoclassical economics is simply closed off and hence such papers can't exist, but there are slightly heterodox fields such as evolutionary economics and complexity (in the SFI sense) economics that justify themselves in language familiar to economists. These fields also make similar critiques as the computational complexity approach (such as moving away from assumptions of equilibria), but don't justify them as rigorously as CS does.

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I see two separate directions to take your question. One is How has a computer science philosophy and computational thinking impacted the field of economics, and why should economists care about the computer science approach? This is a really cool but really broad question that I'll avoid attempting to address.

The second is more specific: Now that computer scientists know that many problems in game theory are hard, how do we convince economists that these are important issues with or objections to their work? This may not be what you had in mind, but it seems to be an interpretation of what you wrote, so I want to address it because I think it's a bit problematic and I think there are reasons not to write an essay arguing this point (which might explain any lack of answers).

First, micro-economists are often theorists and they may be more interested in understanding the problem in their model than in ours. There is no a priori reason one approach is better than the other. As an analogy, many theoretical computer scientists are happy to design algorithms that work over real numbers even though this may require undecidable operations. Similarly, to an economist, complexity may be a detail that clouds one's understanding of what's important in their model rather than a key consideration. This seems more a matter of preference or philosophy than right or wrong.

Second, it's not clear that computer science is yet in a position to argue convincingly that our models fit the real world better than theirs, until we have experimental data to back this up. (After all, it might be for example that markets often find equilibria quickly in practice, so hardness of computing is irrelevant to real-world applications.) Without data, the disagreement is philosophical and it's hard to claim there is a right or wrong side. I don't know that we have enough data yet to make any specific claims.

Third, I think many economists to whom these issues are relevant have been taking notice. In areas like matching, for example (subject of last year's Nobel!), a computational complexity and algorithmic approach is important as they attempt to implement solutions at large scale. So if an economist claims that complexity isn't relevant to her interests, she might be right; but there are others who do take notice.

So in sum, while it seems like a worthwhile goal to help make economists aware of the results regarding complexity in economics (especially as some do take interest), I am not sure that we are in a position to argue that they should take much notice or change their approach; and I think a strong scientific argument would require more data rather than just philosophy.