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The Properties of Conjectural Variations in the Nonlinear Stackelberg Oligopoly Model

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.

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Correspondence to M. I. Geraskin.

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This paper was recommended for publication by M. V. Gubko, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 6, pp. 105–130.

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Geraskin, M.I. The Properties of Conjectural Variations in the Nonlinear Stackelberg Oligopoly Model. Autom Remote Control 81, 1051–1072 (2020). https://doi.org/10.1134/S0005117920060089

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Keywords

  • oligopoly
  • Stackelberg game
  • power cost function
  • multilevel leadership