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Avtomatika i Telemekhanika, 2020, Issue 6, Pages 105–130
DOI: https://doi.org/10.31857/S0005231020060074
(Mi at15350)
 

This article is cited in 15 scientific papers (total in 15 papers)

Control in Social Economic Systems

The properties of conjectural variations in the nonlinear Stackelberg oligopoly model

M. I. Geraskin

Samara National Research University, Samara, Russia
References:
Abstract: The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. The conjectural variations of each agent, i.e., the expected responses (changes in actions) of his counteragents that optimize their utility functions, are studied. Formulas for calculating the conjectural variations of each agent and also the sum of the conjectural variations of all agents in the environment of each agent are derived. The signs of conjectural variations under an arbitrary level of Stackelberg leadership are analyzed. The following properties of conjectural variations are established: 1) the variations are negative if the cost functions of all environmental agents are either convex or concave; 2) the variations are positive if the agents with concave cost functions (the ones with the positive scale effect) prevail in the environment over the agents with convex cost functions (the ones with the negative scale effect). The sum of the agent's conjectural variations is: 1) negative and its magnitude is bounded above by 1 if the environmental agents mainly have convex cost functions; 2) positive and unlimited if the agents with concave cost functions prevail in the environment.
Keywords: oligopoly, Stackelberg game, power cost function, multilevel leadership.
Presented by the member of Editorial Board: M. V. Goubko

Received: 23.09.2019
Revised: 25.12.2019
Accepted: 30.01.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 6, Pages 1051–1072
DOI: https://doi.org/10.1134/S0005117920060089
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. I. Geraskin, “The properties of conjectural variations in the nonlinear Stackelberg oligopoly model”, Avtomat. i Telemekh., 2020, no. 6, 105–130; Autom. Remote Control, 81:6 (2020), 1051–1072
Citation in format AMSBIB
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\transl
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\pages 1051--1072
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  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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