×

Learning cycles in Bertrand competition with differentiated commodities and competing learning rules. (English) Zbl 1402.91076

Summary: This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.

MSC:

91A26 Rationality and learning in game theory
91A40 Other game-theoretic models
91A25 Dynamic games
91B24 Microeconomic theory (price theory and economic markets)
91B54 Special types of economic markets (including Cournot, Bertrand)
91B55 Economic dynamics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Anufriev, M., Bao, T., Tuinstra, J., 2013. Fund choice behavior and estimation of switching models: an experiment. CeNDEF working paper 13-04.
[2] Anufriev, M.; Hommes, C., Evolutionary selection of individual expectations and aggregate outcomes in asset pricing experiments, American Economic JournalMicroeconomics, 4, 35-64, (2012)
[3] Arrow, K.; Hurwicz, L., Stability of the gradient process in n-person games, Journal of the Society for Industrial and Applied Mathematics, 8, 280-294, (1960) · Zbl 0101.37104
[4] Bischi, G. I.; Chiarella, C.; Kopel, M.; Szidarovszky, F., Nonlinear oligopoliesstability and bifurcations, (2009), Springer
[5] Bischi, G. I.; Mammana, C.; Gardini, L., Multistability and cyclic attractors in duopoly games, Chaos, Solitons & Fractals, 11, 543-564, (2000) · Zbl 0960.91017
[6] Bonanno, G., Oligopoly equilibria when firms have local knowledge of demand, International Economic Review, 29, 45-55, (1988) · Zbl 0689.90008
[7] Bonanno, G.; Zeeman, E. C., Limited knowledge of demand and oligopoly equilibria, Journal of Economic Theory, 35, 276-283, (1985) · Zbl 0597.90014
[8] Brock, W.; Hommes, C., A rational route to randomness, Econometrica, 65, 1059-1095, (1997) · Zbl 0898.90042
[9] Brousseau, V.; Kirman, A., Apparent convergence of learning processes in mis-specified games, (Dutta, B.; Mookherjee, D.; Parthasarathy, T.; Raghavan, T.; Ray, D.; Tijs, S., Game Theory and Economic Applications, (1992), Springer-Verlag) · Zbl 0803.90026
[10] Corchon, L.; Mas-Colell, A., On the stability of best reply and gradient systems with applications to imperfectly competitive models, Economics Letters, 51, 59-65, (1996) · Zbl 0875.90004
[11] Cressman, R., Evolutionary dynamics and extensive form games, (2003), The MIT Press · Zbl 1067.91001
[12] Droste, E.; Hommes, C.; Tuinstra, J., Endogenous fluctuations under evolutionary pressure in Cournot competition, Games and Economic Behavior, 40, 232-269, (2002) · Zbl 1031.91013
[13] Erev, I.; Ert, E.; Roth, A. E., A choice prediction competition for market entry games: an introduction, Games, 1, 117-136, (2010) · Zbl 1311.91075
[14] Evans, G.; Honkapohja, S., Learning and expectations in macroeconomics, (2001), Princeton University Press
[15] Fudenberg, D.; Levine, D., The theory of learning in games, (1998), The MIT press
[16] Furth, D., Stability and instability in oligopoly, Journal of Economic Theory, 40, 197-228, (1986) · Zbl 0627.90011
[17] Gal-Or, E., First mover and second mover advantages, International Economic Review, 26, 649-653, (1985) · Zbl 0573.90106
[18] Gates, D.; Rickard, J.; Wilson, D., A convergent adjustment process for firms in competition, Econometrica, 45, 1349-1363, (1977) · Zbl 0363.90033
[19] Kirman, A., Mistaken beliefs and resultant equilibria, (Frydman, R.; Phelps, E., Individual Forecasting and Collective Outcomes, (1983), Cambridge University Press), 147-166
[20] Kopányi, D., Heterogeneous learning in bertrand competition with differentiated goods, (Teglio, A.; Alfarano, S.; Camacho-Cuena, E.; Ginés-Vilar, M., Managing Market ComplexityThe Approach of Artificial Economics, (2013), Springer-Verlag), 155-166
[21] Marcet, A.; Sargent, T., Convergence of least squares learning mechanisms in self-referential linear stochastic models, Journal of Economic Theory, 48, 337-368, (1989) · Zbl 0672.90023
[22] Mira, C., Chaotic dynamicsfrom the one-dimensional endomorphism to the two-dimensional diffeomorphism, (1987), World Scientific
[23] Offerman, T.; Potters, J.; Sonnemans, J., Imitation and belief learning in an oligopoly experiment, Review of Economic Studies, 69, 973-997, (2002) · Zbl 1046.91051
[24] Roth, A.; Erev, I., Learning in extensive-form gamesexperimental data and simple dynamic models in the intermediate term, Games and Economic Behavior, 8, 164-212, (1995) · Zbl 0833.90144
[25] Stahl, D., Boundedly rational rule learning in a guessing game, Games and Economic Behavior, 16, 303-330, (1996) · Zbl 0863.90140
[26] Stock, J.; Watson, M., Introduction to econometrics, (2003), Addison Wesley
[27] Tuinstra, J., A price adjustment process in a model of monopolistic competition, International Game Theory Review, 6, 417-442, (2004) · Zbl 1102.91315
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.