Abstract
An agent-based model is used to determine market equilibrium with price-setting firms in an oligopoly market. The agent-based model is designed to match the experimental rules that Brandts and Guillen (J Ind Econ 55:453–474, 2007) used with human subjects. Their model uses posted prices and advance production of a perishable good. When the marginal cost is zero, the analytical Bertrand solution is almost perfect competition. When the marginal cost is nonzero, the game does not have a theoretical equilibrium in pure strategies. The agent-based model results show that with one or two firms, prices are at or near the monopoly level, which matches the human experiments. With four firms, prices are always at the perfectly competitive level when particle swarm optimization is used. Results using a genetic algorithm, however, are noisier than those using the particle swarm optimization, and the genetic algorithm falls short of the competitive solution. The triopoly market changes from mostly monopoly to a price in between monopoly and perfect competition when a marginal cost is added. The computerized agents tend to overproduce so that profits are negative in the three- and four-firm cases when production is costly. While the prices in the simulation are close to those observed in experiments with human subjects, the inefficiency due to overproduction is much greater in the agent-based model results. This result suggests that human agents are able to reach solutions, perhaps through social norms, that are missed by the simple agent-based rules used here.
Similar content being viewed by others
References
Altavilla C, Luini L, Sbriglia P (2006) Social learning in market games. J Econ Behav Organ 61: 632–652
Anderson EJ, Cau TDH (2009) Modeling implicit collusion using coevolution. Oper Res 57: 439–455
Arifovic J (1994) Genetic algorithm learning and the Cobweb-model. J Econ Dyn Control 18: 3–28
Arifovic J (1996) The behavior of the exchange rate in the genetic algorithm and experimental economies. J Political Econ 104: 510–541
Axelrod R (1987) The evolution of strategies in the iterated prisoner’s dilemma. In: Davis LD (eds) Genetic algorithms and simulated annealing. Pitman, London, pp 32–41
Brandts J, Guillen P (2007) Collusion and fights in an experiment with price-setting firms and advance production. J Ind Econ 55: 453–474
Davis DD (2002) Strategic interactions, market information and predicting the effects of mergers in differentiated product markets. Int J Ind Organ 20: 1277–1312
Dufwenberg M, Gneezy U (2000) Price competition and market concentration: an experimental study. Int J Ind Organ 18: 7–22
Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micromachine and human science, Nagoya, Japan, pp 39-43
Erev I, Roth A (1998) Predicting how people play games: reinforcement learning in experimental games with unique mixed strategy equilibria. Am Econ Rev 88: 848–881
Fouraker LE, Siegel S (1963) Bargaining behavior. McGraw-Hill, London
Gintis H (2009) Towards a renaissance of economic theory. J Econ Behav Organ 73: 34–40
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA
Huck S, Normann H, Oechssler J (2004) Two are few and four are many: number effects in experimental oligopolies. J Econ Behav Organ 53: 435–446
Kimbrough SO, Murphy FH (2009) Learning to collude tacitly on production levels by oligopolistic agents. Comput Econ 33: 47–78
Kutschinski E, Uthmann T, Polani D (2003) Learning competitive pricing strategies by multi-agent reinforcement learning. J Econ Dyn Control 27: 2207–2218
Simon HA (1991) Bounded rationality and organizational learning. Organ Sci 2: 125–134
Smith VL (2009) Theory and experiment: what are the questions?. J Econ Behav Organ 73: 3–15
Suetens S, Potters J (2007) Bertrand colludes more than Cournot. Exp Econ 10: 71–77
Vriend JN (2000) An illustration of the essential difference between individual and social learning, and its consequences for computational analyses. J Econ Dyn Control 24: 1–19
Waltman L, Kaymak U (2008) Q-learning agents in a Cournot oligopoly model. J Econ Dyn Control 32: 3275–3293
Zhang T, Brorsen BW (2009) Particle swarm optimization algorithm for agent-based artificial markets. Comput Econ 34: 399–417
Zhang T, Brorsen BW (2010) The long-run and short-run impact of captive supplies on the spot market price: an agent-based artificial market. Am J Agric Econ 92: 1181–1194
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, T., Brorsen, B.W. Oligopoly firms with quantity-price strategic decisions. J Econ Interact Coord 6, 157–170 (2011). https://doi.org/10.1007/s11403-011-0081-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11403-011-0081-2