Abstract
Classical oligopoly theory has strong analytical foundations but is weak in capturing the operating environment of oligopolists and the available knowledge they have for making decisions, areas in which the management literature is relevant. We use agent-based models to simulate the impact on firm profitability of policies that oligopolists can pursue when setting production levels. We develop an approach to analyzing simulation results that makes use of nonparametric statistical tests, taking advantage of the large amounts of data generated by simulations, and avoiding the assumption of normality that does not necessarily hold. Our results show that in a quantity game, a simple exploration rule, which we call Probe and Adjust, can find either the Cournot equilibrium or the monopoly solution depending on the measure of success chosen by the firms. These results shed light on how tacit collusion can develop within an oligopoly.
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Alkemade F., La Poutr H., Amman H.M. (2006) Robust evolutionary algorithm design for socio-economic simulation. Computational Economics 28(4): 355–370
Arifovic J. (1994) Genetic algorithm learning and the cobweb model. Journal of Economic Dynamics and Control 18(1): 3–28
Arifovic, J., & Maschek, M. K. (2005). Social vs. individual learning: What makes a difference? Working Paper, Simon Fraser University.
Axelrod R. (1984) The evolution of cooperation. Basic Books, Inc., New York, NY
Barr J., Saraceno F. (2005) Cournot competition, organization and learning. Journal of Economics Dynamics and Control 29(1): 277–295
Battalio R., Samuelson L., Van Huyck J. (2001) Optimization incentives and coordination failure in laboratory stag hunt games. Econometrica 69(3): 749–764
Brandenberger A.M., Nalebuff B.J. (1996) Co-Opetition: A revolution mindset that combines competition and cooperation: The Game theory strategy that’s changing the game of business. Doubleday, New York, NY
Brenner, T. (eds) (1999a) Computational techniques for modelling learning in economics. Kluwer Academic Publishers, Boston, MA
Brenner T. (1999b). Modelling learning in economics. Cheltenham, UK: Edward Elgar
Brenner T. (2006) Agent learning representation: Advice on modelling economic learning. In: Tesfatsion L., Judd K.L (eds) Handbook of computational economics. Agent-based computational economics, handbooks in economics Vol. 2. North-Holland, Amsterdam, The Netherlands, pp. 895–948
Bruun, C. (eds) (2006) Advances in artificial economics. Lecture notes in economics and mathematical systems (Vol. 584). Springer, Berlin, Germany
Bunn D.W., Oliveira F. (2003) Evaluating individual market power in electricity markets via agent-based simulation. Annals of Operations Research 121: 57–78
Camerer C.F. (2003) Behavioral game theory: Experiments in strategic interaction. Russell Sage Foundation and Princeton University Press, New York, NY and Princeton, NJ
Carpenter J.P. (2002) Evolutionary models of bargaining: Comparing agent-based computational and analytical approaches to understanding convention evolution. Computational Economics 19(1): 25–49
Dawid H., Dermietzel J. (2006) How robust is the equal split norm? On the de-stabilizing effect of responsive strategies. Computational Economics 28: 371–397
Duffy J. (2006) Agent-based models and human subject experiments. In: Tesfatsion L., Judd K.L. (eds) Handbook of computational economics Agent-based computational Economics, handbooks in Economics Vol. 2. North-Holland, Amsterdam The Netherlands, pp. 949–1012
Entriken, R., & Wan, S. (2005). Agent-based simulation of an automatic mitigation procedure. In Proceedings of the 38th Hawaii International Conference on System Sciences.
Hommes, C. H., Sonnemans, J., Tuinstra, J., & Velden, H. V. (2003). Learning in cobweb experiments. Working Paper TI 2003-020/1, University of Amsterdam, Tinbergen Institute.
Huck S., Normann H.-T., Oechssler J. (2003) Zero-knowledge cooperation in dilemma games. Journal of Theoretical Biology 220: 47–54
Huck S., Normann H.-T., Oechssler J. (2004) Two are few and four are many: Number effects in experimental oligopolies. Journal of Economic Behavior & Organization 53: 435–446
Kagel, J.H., Roth, A.E. (eds) (1995) The handbook of experimental economics. Princeton University Press, Princeton, NJ
Kimbrough, S. O., & Lu, M. (2005). Simple reinforcement learning agents: Pareto beats Nash in an algorithmic game theory study. Information Systems and e-Business, 3(1), 1-19. http://dx.doi.org/10.1007/s10257-003-0024-0.
Kimbrough S.O., Lu M., Kuo A. (2005) A note on strategic learning in policy space. In: Kimbrough S.O., Wu D.J. (eds) Formal modelling in electronic commerce: Representation, inference, and strategic interaction. Springer, Berlin, Germany, pp. 463–475
Kimbrough S.O., Lu M., Murphy F. (2005) Learning and tacit collusion by artificial agents in Cournot duopoly games. In: Kimbrough S.O., Wu D.J. (eds) Formal modelling in electronic commerce. Springer, Berlin, Germany, pp. 477–492
Kuenne R.E. (1998) Price and nonprice rivalry in oligopoly: The integrated battleground. St. Martins Press, New York, NY
Marks R. (2006) Market design using agent-based models. In: Tesfatsion L., Judd K.L. (eds) Handbook of computational economics. Agent-based computational economics, handbooks in economics Vol. 2. North-Holland, Amsterdam, The Netherlands, pp. 1339–1380
Marks, R. E., & Midgley, D. F. (2006). Using evolutionary computing to explore social phenomena: Modeling the interactions between consumers, retailers and brands. Working Paper, Australian Graduate School of Management.
Midgley D.F., Marks R.E., Cooper L.G. (1997) Breeding competitive strategies. Management Science 43(3): 257–275
Nagle T.T., Hogan J.E. (2006) The strategy and tactics of pricing: A guide to growing more profitably (4th ed.). Pearson/Prentice Hall, Upper Saddle River, NJ
Pyka, A., & Fagiolo, G. (2005). Agent based modeling: A methodology for neo-Shumpeterian economics. Working Paper 272, University of Augsburg.
R Development Core Team (2007). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
Riechmann, T. (2002). Cournot or Walras? Agent based learning, rationality, and long run results in oligopoly games. Discussion Paper 261, University of Hannover, Faculty of Economics, Königsworther Platz 1, 30 167 Hannover, Germany.
Sallans, B., Pfister, A., Karatzoglou, A., & Dorffner, G. (2003). Simulation and validation of an integrated markets model. Journal of Artificial Societies and Social Simulation, 6(4). http://jasss.soc.surrey.ac.uk/6/4/2.html
Selten, R., Mitzkewitz, M., & Uhlich, G. R. (1997). Duopoly strategies programmed by experienced players. Econometrica, 65(3), 517–555.
Skyrms, B. (2001). The stag hunt. Proceedings and Addresses of the American Philosophical Association, 75(2), 31–41.
Skyrms B. (2004) The stag hunt and the evolution of social structure. Cambridge University Press, Cambridge, UK
Tesfatsion L. (2006) Agent-based computational economics: A constructive approach. In: Tesfatsion L., Judd K.L. (eds) Handbook of computational economics Agent-based computational economics, handbooks in economics Vol. 2. North-Holland, Amsterdam, The Netherlands, pp. 831–880
Tesfatsion, L., Judd, K.L. (eds) (2006) Handbook of computational economics Agent-based computational economics, handbooks in economics. North-Holland, Amsterdam, The Netherlands
Vriend N.J. (2000) An illustration of the essential difference between individual learning and social learning and its consequences for computational analysis. Journal of Economic Dynamics and Control 24: 1–19
Waltman, L., & Kaymak, U. (2005). Q-learning agents in a Cournot oligopoly model. Working Paper, Erasmus University, Faculty of Economics, Rotterdam.
Winston W.L. (2004) Operations research applications and algorithms (4th ed.). Brooks/Cole, Belmont, CA
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Kimbrough, S.O., Murphy, F.H. Learning to Collude Tacitly on Production Levels by Oligopolistic Agents. Comput Econ 33, 47–78 (2009). https://doi.org/10.1007/s10614-008-9150-6
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DOI: https://doi.org/10.1007/s10614-008-9150-6