Tripoly Stackelberg game model: One leader versus two followers

S.S. Askar

Applied Mathematics and Computation, 2018, vol. 328, issue C, 301-311

Abstract: This paper is devoted to introduce and study a Stackelberg game consisting of three competed firms. The three firms are classified as a leader which is the first firm and the other two firms are called the followers. A linear inverse demand function is used. In addition a quadratic cost based on an actual and announced quantities is adopted. Based on bounded rationality, a three-dimensional discrete dynamical system is constructed. For the system, the backward induction is used to solve the system and to get Nash equilibrium. The obtained results are shown that Nash equilibrium is unique and its stability is affected by the system’s parameters by which the system behaves chaotically due to bifurcation and chaos appeared. Some numerical experiments are performed to portrays such chaotic behavior. A control scheme is used to return the system back to its stability state and is supported by some simulations.

Keywords: Bounded rationality; Stackelberg game; Stability; Bifurcation; Chaos; Control (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:328:y:2018:i:c:p:301-311

DOI: 10.1016/j.amc.2018.01.041

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