An Agent-Based Simulation of the Stolper–Samuelson Effect


We demonstrate that agent-based simulations can exhibit results in line with classic macroeconomic theory. In particular, we present an agent-based simulation of an Arrow–Debreu economy that accurately exhibits the Stolper–Samuelson effect as an emergent property. Absent of a Walrasian auctioneer or any other central coordination, we let firm and consumer agents of different types interact in an open, money-driven market. Exogenous preference shocks result in price and wage shifts that are in accordance with the general equilibrium solution, not only qualitatively but also quantitatively with high accuracy. Key to this achievement are three independent measures. First, we overcome the poor input synchronization of conventional price finding heuristics of firms in agent-based models by introducing sensor prices, a novel approach to price finding that decouples information exploitation from information exploration. Second, we improve accuracy and convergence by employing exponential search as exploration algorithm. Third, we normalize prices indirectly by fixing dividends, thereby stabilizing the system’s dynamics.

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  1. 1.

    Originally, the theorem was only shown to hold for two inputs and two outputs, with constant returns to scale and constant supply of inputs. While Jones and Scheinkman (1977) generalized it to larger number of inputs and outputs, the Stolper–Samuelson effect is not guaranteed to appear when returns to scale are not constant (Jones 1968) or supply of inputs is variable (Martin 1976), both of which is the case in our model. Nonetheless, the effect is present in the discussed settings thanks to their parametric symmetry.

  2. 2.

    With threshold \(\tau \), total dividends of n firms f with cash \(c_f\) each are \(d_{tot} = \sum _f (c_f - \tau ) = \sum _f c_f - n \tau \), which is constant.

  3. 3.

    A quick path to this insight is to imagine the consumer being endowed with one gold nugget of market price d instead of dividends d. This yields the same outcome, yet transforms d into a price that must be—like every price— proportional to the general price level.

  4. 4.

    To be precise, Riccetti et al. randomize the percentage approach, i.e. \(p_{t+1} = (1\pm s) p_t\) with s uniformely distributed, leading to a forth variant not discussed here.


  1. Arrow, K. J., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica, 22(3), 265–290.

    Article  Google Scholar 

  2. Axtell, R. (2005). The complexity of exchange. The Economic Journal, 115(504), F193–F210.

    Article  Google Scholar 

  3. Bentley, J. L., & Yao, A. C. C. (1976). An almost optimal algorithm for unbounded searching. Information Processing Letters, 5(3), 82–87.

    Article  Google Scholar 

  4. Brock, W. A., & Hommes, C. (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control, 22(8), 1235–1274.

    Article  Google Scholar 

  5. Bruno, R. (2015). Version control systems to facilitate research collaboration in economics. Computational Economics. doi:10.1007/10614-015-9513-8.

  6. Catalano, M., & Di Guilmi, C. (2015). Dynamic stochastic generalised aggregation in a multisectoral macroeconomic model. In Proceedings of the 21st International Conference on Computing in Economics and Finance (CEF 2015).

  7. Coase, R. H. (1937). The nature of the firm. Economica, 4(16), 386–405.

    Article  Google Scholar 

  8. Deissenberg, C., Van Der Hoog, S., & Dawid, H. (2008). Eurace: A massively parallel agent-based model of the european economy. Applied Mathematics and Computation, 204(2), 541–552.

    Article  Google Scholar 

  9. Eidson, E. D., & Ehlen, M. A. (2005). NISAC agent-based laboratory for economics (N-ABLETM): Overview of agent and simulation architectures. Technical Report SAND2005-0263, Sandia National Laboratories.

  10. Elmaghraby, W., & Keskinocak, P. (2003). Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions. Management Science, 49(10), 1287–1309.

    Article  Google Scholar 

  11. Feldman, A. M. (1973). Bilateral trading processes, pairwise optimality, and pareto optimality. The Review of Economic Studies, 40, 463–473.

    Article  Google Scholar 

  12. Gatti, D. D., Desiderio, S., Gaffeo, E., Cirillo, P., & Gallegati, M. (2011). Macroeconomics from the bottom-up (Vol. 1). New York: Springer Science & Business Media.

    Google Scholar 

  13. Gintis, H. (2007). The dynamics of general equilibrium. The Economic Journal, 117(523), 1280–1309.

    Article  Google Scholar 

  14. Hommes, C. (2013). Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge: Cambridge University Press.

    Google Scholar 

  15. Jones, R. W. (1968). Variable returns to scale in general equilibrium theory. International Economic Review, 9(3), 261–272.

    Article  Google Scholar 

  16. Jones, R. W., & Scheinkman, J. A. (1977). The relevance of the two-sector production model in trade theory. The Journal of Political Economy, 85, 909–935.

    Article  Google Scholar 

  17. Kim, D. H. (1992). Guidelines for drawing causal loop diagrams. The Systems Thinker, 3(1), 5–6.

    Google Scholar 

  18. LeBaron, B. (2001). Empirical regularities from interacting long-and short-memory investors in an agent-based stock market. IEEE Transactions on Evolutionary Computation, 5(5), 442–455.

    Article  Google Scholar 

  19. Martin, J. P. (1976). Variable factor supplies and the Heckscher–Ohlin–Samuelson model. The Economic Journal, 86(344), 820–831.

    Article  Google Scholar 

  20. Milgrom, P., & Roberts, J. (1994). Economics, organization and management. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  21. Negishi, T. (1972). General equilibrium theory and international trade. North-Holland Publishing Company: Amsterdam.

    Google Scholar 

  22. Riccetti, L., Russo, A., & Gallegati, M. (2015). An agent based decentralized matching macroeconomic model. Journal of Economic Interaction and Coordination, 10(2), 305–332.

    Article  Google Scholar 

  23. Rouchier, J. (2013). The interest of having loyal buyers in a perishable market. Computational Economics, 41(2), 151–170.

    Article  Google Scholar 

  24. Seppecher, P. (2012). Jamel: A java agent-based macroeconomic laboratory. doi:10.2139/ssrn.2669488.

  25. Stolper, W. F., & Samuelson, P. A. (1941). Protection and real wages. The Review of Economic Studies, 9(1), 58–73.

    Article  Google Scholar 

  26. Tesfatsion, L. (2006). Agent-based computational economics: A constructive approach to economic theory. Handbook of Computational Economics, 2, 831–880.

    Article  Google Scholar 

  27. Wolffgang, U. (2015). A multi-agent non-stochastic economic simulator. In Proceedings of the 21st International Conference on Computing in Economics and Finance (CEF 2015).

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We would like to thank Johannes Brumm and Gregor Reich for their valuable inputs, Abraham Bernstein for pointing us to system dynamics, Krzysztof Kuchcinski and Radoslaw Szymanek for the JaCoP solver, and participants of CEF 2015 – most notably Ulrich Wolffgang – for their helpful comments.

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Correspondence to Luzius Meisser.

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Meisser, L., Kreuser, C.F. An Agent-Based Simulation of the Stolper–Samuelson Effect. Comput Econ 50, 533–547 (2017).

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  • Computational economics
  • Agent-based economics
  • Price finding
  • Price normalization
  • Sensor prices
  • System dynamics