Abstract
We present the Stackelberg model with linear demand and cost functions for the agents where the leader agent and follower agents have imprecise initial information regarding the marginal costs of competitors. Agents dynamically refine their perceptions and actions based on observing the actions other agents. We obtain necessary and sufficient conditions of the event that the dynamic converges to a Stackelberg equilibrium with true values of marginal costs. We also clarify the situations when agents cannot come to an equilibrium.
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References
Vasin, A.A., Vasina, A.A., and Ruleva, A.Yu., On Organizing Markets of Homogeneous Goods, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2007, no. 1, pp. 98–112.
Novikov, D.A., Models of Strategic Behavior, Autom. Remote Control, 2012, vol. 73, no. 1, pp. 1–19.
Opoitsev, V.I., Ravnovesie i ustoichivost’ v modelyakh kollektivnogo povedeniya (Equilibrium and Stability in Models of Collective Behavior), Moscow: Nauka, 1977.
Vasin, A.A., Modeli dinamiki kollektivnogo povenediya (Models of Collective Behavior Dynamics), Moscow: Mosk. Gos. Univ., 1989.
Algazin, G.I. and Algazina, D.G., Information Equilibrium in the Model of Collective Behavior Dynamics on a Competitive Market, Upravlen. Bol’shimi Sist., 2016, no. 64, pp. 112–136.
Bulavskii, V.A. and Kalashnikov, V.V., Single-Parameter Run Method for Studying Equilibrium States, Ekonom. Mat. Metody, 1994, vol. 30, no. 4, pp. 129–138.
Novikov, D.A., Dynamics of a System with Large Number of Purposeful Elements, Autom. Remote Control, 1996, vol. 57, no. 2, pp. 302–304.
Puu, T., Attractors, Difurcations, & Chaos: Nonlinear Phenomena in Economics, Springer: Berlin, 2003.
Dusouchet, O.M., Static Cournot–Nash Equilibria and Strategic Reflective Games of Oligopoly: A Case of Linear Functions of Demand and Costs, Ekon. Zh. Vyssh. Shkol. Ekon., 2006, no. 1, pp. 3–32.
Algazin, G.I. and Algazina, Yu.G., Modeling the Behavior of Economic Agents in a “Producer–Mediator–Competitive Market” System, Upravlen. Bol’shimi Sist., 2011, no. 32, pp. 83–108.
Novikov, D.A. and Chkhartishvili, A.G., Reflexion and Control: Mathematical Models, Leiden: CRC Press, 2014.
Markushevich, A.A., Vozvratnye posledovatel’nosti (Reflexive Sequences), Moscow: Gos. Izd. Tekhn.-Teoret. Lit., 1950.
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Original Russian Text © G.I. Algazin, D.G. Algazina, 2017, published in Avtomatika i Telemekhanika, 2017, No. 9, pp. 91–105.
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Algazin, G.I., Algazina, D.G. Collective behavior in the Stackelberg model under incomplete information. Autom Remote Control 78, 1619–1630 (2017). https://doi.org/10.1134/S0005117917090077
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DOI: https://doi.org/10.1134/S0005117917090077