Is the mainstream against agent based modelling? I have heard it said that mainstream economists disapprove of agent based modelling and some of the most prestigious economics journals will not accept papers that employ them. Is this true? And if so, why?
I'm an outsider, so I can't speak of what the boards of prestigious economic journals think of this, but...

I suspect it has something to do with the opacity of computer simulations using agent-based models (ABM) compared to math proofs or even the statistical models that are the staple of applied econometrics... although simpler computer simulations like Monte Carlo methods are well accepted. 

E.g. Arnold Kling, who has some academic and some Federal Reserve credentials, writes


  My concern with ABM is getting a result and not really knowing why you got it. Alternatively, if you really understand how the ABM is getting its result, you should be able to show how to get that results in a simple model, perhaps with a numerical example.


He doesn't seem to be on the board of any journals, but I doubt his opinion is uncommon.

BoE economist A. Turrell has written a (lengthier) paper containing a fairly balanced (IMO) list of pros and cons of ABM. "Calibration and interpretation" takes most space there when it comes weaknesses. He also mentions the Lucas critique as relevant, and notes that the most fertile cases for ABM being behavioral-economics oriented, e.g. using bounded rationality, also makes them most difficult to proof against the Lucas critique.



At least currently, the staple of macro-economics models is DSGE, which nearly always include a representative-agent:


  All the different views mainstream macroeconomists have about the state of their field and about possible areas of improvement should not diminish the degree to which they converged methodologically in studying fluctuations. They all analyse such phenomena usually through a dynamic stochastic general equilibrium model with a representative agent, firmly grounded on microeconomic principles. Moreover, several of them agree with Chari (2010: 2) that “any interesting model must be a dynamic stochastic general equilibrium model. From this perspective, there is no other game in town.” Therefore, he continues, “a useful aphorism in macroeconomics is: ‘If you have an interesting and coherent story to tell, you can tell it in a DSGE model. If you cannot, your story is incoherent.’”


Generally DSGE models assume a representative agent (in part because they need to side-step Sonnenschein–Mantel–Debreu type results).


  The theorems of Hugo Sonnenschein, Rolf Mantel and Gerard Debreu in the early 1970s established that the restrictions that generate well-behaved individual demand functions do not constrain aggregate demand functions to exhibit the same properties [...]. The new classicals sidestepped the problem of aggregation either by imagining an economy composed of identical individuals or by assuming that there is one individual who represents the whole economy, so that the solution to the optimization problem of this representative agent gives the aggregate relationships in that economy.


There were more steps before the current new synthesis DSGE approach, but I don't want to get into that here. My point with this is that if you have an optimizing representative-agent (RA), you don't need much computer/behavioral simulation... Of course, RA models are criticized (Fagiolo and Roventini summarize RA/DSGE criticism from much more famous economists, Stiglitz etc.) exactly because of this, e.g. their inability to predict (or supposedly even explain) the Great Recession etc. But this criticism seems to not be enough to dislodge DSGE from the current mainstream macro, presently. (There is a bit more subtlety to RA than what I've covered here; RA can include some sources of parametric heterogeneity but assumes a sort of "structural" homogeneity, if I understand that correctly.)

Fagiolo and Roventini have a detailed comparison of DGSE with ACE/ABM  approaches, and while they find that the two approaches share some criticism, they point out the following difference:


  The last issue worth mentioning is specific to ACE and it concerns the comparability of
  different agent-based models. DSGE models are all built using a commonly-shared set of behavioral
  rules (e.g., representative agents solving a stochastic dynamic optimization problems)
  and their empirical performance is assessed with common techniques (i.e., VAR models). This
  allows to develop a common protocol about "how to do macroeconomics with DSGE models"
  and it eases the comparison of the results produced by competing models. Given the relatively
  infancy of the ACE paradigm, the lack of such a widespread agreement among the ACE community
  hinders the dialogue among different ABMs, reducing the comparability of their results,
  and possibly slowing down new developments. In that respect, the development of common
  documentation guidelines (Wolf et al., 2013a), dedicated languages and platforms can surely
  improve the situation, increase the exchanges among ACE scholars, and reduce the entry cost
  to agent-based modeling.


In other words, because of its infancy, there's a lack of standardization in ACE/ABM (unlike DSGE), which presently also hinders wider adoption for the former. (As minor point of terminology, they use ACE/ABM interchangeably: "ACE [agent-based computational economics] models (often called agent-based models,
ABMs)".)