Game-theoretic analysis of Stackelberg oligopoly with arbitrary rank reflexive behavior of agents

Abstract

Purpose This paper aims to consider the problem of determining the equilibriums on oligopoly market in case of Stackelberg leader (leaders) and reflexive behavior of market agents. Design/methodology/approach This paper includes economic and mathematical modeling, optimization methods and game theory. Findings This paper explains models of reflexive games on oligopoly market, taking into account the diversity of agents’ reasoning about strategies of environing and equilibrium mechanisms for coincidence or opposition of agents’ reflexive reasoning on the same rank of reflection. Research limitations/implications This paper considers the oligopoly market with linear function of demand and costs of agents, the rational behavior of agents and the reflexive reasoning on the same rank of reflection. The set of agents’ reasoning about the environing strategies is considered as a set of market states for which the problem of agent’s optimal action choosing solves with the complete awareness. Practical implications Identification of reflexive behavior of environing allows agents to increase their market shares and profit. Social implications Oligopoly markets play a leading role in the world oil trade and reflexive behavior affects the market equilibrium. Originality/value In the paper, the mechanisms of equilibrium in reflexive games on the linear duopoly market for arbitrary rank reflection are developed.