Agent-based models

Science as Grand Theft Auto

…comprise a particular emphasis within the broad field of simulating stuff. An agent based simulation designed to approximate the behaviour of some real-world system will tend to eschew partial differential equations or fixed-point proofs in favour of, say, breaking down a large system into the component chunks that make it up. If we were looking at a simulation of an economy, an agent-based version might start from the individual humans buys and selling within that economy. Within that simulation we might be interested in working out, say, ‘given what we know about humans and can simulate, what does that tell us about markets’? “Bottom-up” modeling would be a more suggestive name.

Examples

Nicky Case, Overfishing versus ghost whales

Nicky Case, Overfishing versus ghost whales

  • Roll your own using Nicky Case’s Emoji protoype.

  • Nobel Laureate, Thomas Schelling’s 1969 Racial segregation model based on checkers pieces

  • Finite Element Models for simulating the behaviour of materials (e.g. at CSIRO or the National Crash Analysis Centre, these get called agent based models, and although accurate as far as it goes, it smells funny. That’s only one step away from calling all numerical quadrature “agent based modelling”, and then where do our funding applications go?

  • As a kind of primordial ancestor, the classic Ising spin glass model

  • A hypermodern example – EpiCast simulates the entire population of the USA, or at least, a lot more detail about them for disease control than I would have suspected to be reasonable.

Problems of modelling, and what agent-based ones can help with

The problem, the basic problem of science, runs something like this- our current models of system \(X\) with parameter set \(P\) is good at approximating some of the observed behaviours of reality for some range of parameters \(p \subset P\), and that range can be fairly easy to find. However, our model does not seem to be able to produce observed behaviour \(b\) for any value of parameters. Let’s remove some of the simplifying assumptions in our model of \(X\) and make it a more complex model, \(X'\) with more parameters \(P'\), and more diverse behaviours. Now it can possibly produce behaviour \(b\) for some values of of parameters \(p'\subset P'\). But we are no longer assured that we can find the set \(p'\) because of, e.g. loss of nice analytic forms for our model, or because of the curse of dimensionality, and these problems are made worse with every extension of the model.

Typically agent based models come out poorly here because they have vastly more parameters to fit and no more data points to fit them too than anyone else. In macroeconomics, for example, there are a lot more parameters to an economy full of different agents with unique behavioural heuristics and methods of production and technologies etc, than there are when you assume an equilibrium can be reached by some kind of process of aggregating demand and supply functions. Although you can add more parameters to models based on either set of techniques, or devise hybrid models.

These days we have a lot of CPU cycles and a lot of data, at least of some sorts of data, and better fitting algorithms. We can use these to, perhaps, discard some of our simplifying assumptions by producing them as an emergent property of an underlying process, so we have the luxury, perhaps, of keeping agents whose behaviour is harder to simplify, and running the model anyway.

Alternatively, even if we can’t ever hope to fit the model to real data, we can still run models that test out various possible sets of assumptions about behaviour in the hope of getting it at least qualitatively right, and congratulate ourselves that we have not only gotten insight, but preserved ourselves from the danger of mistaking our model of reality for reality itself.

Or we might like to do this because, in some sense, agent-based models are more intuitive, and less abstract, than more mathematical abstractions, and they might give more direct insight into what is happening in a particular situation by letting non-specialists involved participate more directly in devising a model of it. This last option is called companion modelling and it dwells in the dangerous no-man’s-land between science, policy, and community engagement; I for one am terrified of that area. I’d much rather analyse a problem from the outside, be annoyed when no one takes my advice and glean the same sense of righteousness, with much less time and money spent.

Things to be interested in:

  • Agent based models that include realistic constraints of agent attention and search strategies.

  • Economic models that include not only innovation, but plausible representations of the size of innovation search space and the costs of exploring it. This is not necessarily remotely possible.

Now, read:

Axelrod, Robert. 1997a. The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. Princeton University Press.

———. 1997b. “The Dissemination of Culture: A Model with Local Convergence and Global Polarization.” The Journal of Conflict Resolution 41: 203–26. https://doi.org/10.2307/174371.

Bednar, Jenna, and Scott E Page. 2000. “Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Games.”

Bowles, Samuel. 2004. Microeconomics: Behavior, Institutions, and Evolution. Princeton University Press.

Bowles, Samuel, and Herbert Gintis. 2004. “The Evolution of Strong Reciprocity: Cooperation in Heterogeneous Populations.” Theoretical Population Biology 65 (1): 17–28. https://doi.org/10.1016/j.tpb.2003.07.001.

Epstein, Joshua M. 2001. “Learning to Be Thoughtless: Social Norms and Individual Computation.” Computational Economics 18: 9–24. https://doi.org/10.1023/A:1013810410243.

———. 2007. Generative Social Science: Studies in Agent-Based Computational Modeling. Princeton Studies in Complexity. Princeton University Press.

———. 2009. “Modelling to Contain Pandemics.” Nature 460: 687. https://doi.org/10.1038/460687a.

Epstein, Joshua M, John D Steinbruner, and Miles T Parker. 2002. “Modeling Civil Violence: An Agent-Based Computational Approach.” Proceedings of the National Academy of Sciences 99: 7243–50. https://doi.org/10.1073/pnas.092080199.

Gintis, Herbert. 2007. “The Dynamics of General Equilibrium.” The Economic Journal 117 (523): 1280–1309. https://doi.org/10.1111/j.1468-0297.2007.02083.x.

Grimm, Volker, and Steven F Railsback. 2005. Individual-Based Modeling and Ecology: (Princeton Series in Theoretical and Computational Biology). Princeton University Press.

Hailu, Atakelty, and Steven Schilizzi. 2004. “Are Auctions More Efficient Than Fixed Price Schemes When Bidders Learn?” Australian Journal of Management 29: 147–68. https://doi.org/10.1177/031289620402900201.

Henke, Glenn A. 2009. “How Terrorist Groups Survive: A Dynamic Network Analysis Approach to the Resilience of Terrorist Organizations.” ATZL-SWV. ARMY COMMAND AND GENERAL STAFF COLL FORT LEAVENWORTH KS SCHOOL OF ADVANCED MILITARY STUDIES. https://apps.dtic.mil/docs/citations/ADA507988.

Hetzer, Moritz, and Didier Sornette. 2009. “Other-Regarding Preferences and Altruistic Punishment: A Darwinian Perspective.” SSRN Scholarly Paper ID 1468517. Rochester, NY: Social Science Research Network. http://papers.ssrn.com/abstract=1468517.

Horst, Ulrich, Alan Kirman, and Miriam Teschl. 2007. “Changing Identity: The Emergence of Social Groups.” Economics Working Paper 0078. Institute for Advanced Study, School of Social Science. https://ideas.repec.org/p/ads/wpaper/0078.html.

Kirman, Alan. 2010. “Learning in Agent Based Models.”

Latek, Maciej, Robert Axtell, and Bogumil Kaminski. 2009. “Bounded Rationality via Recursion.” In, 457–64. Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.

Lorenz, Jan. 2010. “Heterogeneous Bounds of Confidence: Meet, Discuss and Find Consensus!” Complexity 15 (4): 43–52. https://doi.org/10.1002/cplx.20295.

Lux, Thomas. 2008. “Applications of Statistical Physics in Finance and Economics.” In Applications of Statistical Physics in Finance and Economics. Citeseer.

Ormerod, Paul, and Greg Wiltshire. 2009. “’Binge’ Drinking in the UK: A Social Network Phenomenon.” Mind & Society 8 (2): 135–52. https://doi.org/10.1007/s11299-009-0058-1.

Pluchino, Alessandro, Andrea Rapisarda, and Cesare Garofalo. 2010. “The Peter Principle Revisited: A Computational Study.” Physica A: Statistical Mechanics and Its Applications 389: 467–72. https://doi.org/10.1016/j.physa.2009.09.045.

Riolo, Rick L, Michael D Cohen, and Robert Axelrod. 2001. “Evolution of Cooperation Without Reciprocity.” Nature 414 (6862): 441. https://doi.org/10.1038/35106555.

Rivkin, Jan W. 2001. “Reproducing Knowledge: Replication Without Imitation at Moderate Complexity.” Organization Science, 274–93.

Rosewell, Bridget, and Paul Ormerod. 2004. “How Much Can Firms Know?” Computing in Economics and Finance 2004. https://ideas.repec.org/p/sce/scecf4/44.html.

Smolin, Lee. 2009. “Time and Symmetry in Models of Economic Markets.”

Straatman, Bas, Roger White, and Wolfgang Banzhaf. 2008. “An Artificial Chemistry-Based Model of Economies.” Artificial Life 11: 592.

Tesfatsion, Leigh, and Kenneth L Judd, eds. 2006. Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics. North Holland.

Thurner, Stefan, and Rudolf Hanel. 2010. “Peer-Review in a World with Rational Scientists: Toward Selection of the Average.”

Walker, Brian H, and Marco A Janssen. 2002. “Rangelands, Pastoralists and Governments: Interlinked Systems of People and Nature.” Philosophical Transactions of the Royal Society B: Biological Sciences 357 (1421): 719. https://doi.org/10.1098/rstb.2001.0984.

Weng, L, A Flammini, A Vespignani, F Menczer, L Weng, A Flammini, A Vespignani, and F Menczer. 2012. “Competition Among Memes in a World with Limited Attention.” Scientific Reports 2. https://doi.org/10.1038/srep00335.