ANALYZING AN OPTIMISTIC ATTITUDE FOR THE LEADER FIRM IN DUOPOLY MODELS: A STRONG STACKELBERG EQUILIBRIUM BASED ON A LYAPUNOV GAME THEORY APPROACH

Julio B. Clempner () and Alexander S. Poznyak ()
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Julio B. Clempner: Instituto Politécnico Nacional, Mexico
Alexander S. Poznyak: Center for Research and Advanced Studies

ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 2016, vol. 50, issue 4, 41-60

Abstract: This paper presents a novel game theory approach for representing the Stackelberg dynamic duopoly models. The problem is fitted into a class of ergodic controllable finite Markov chains game. It is consider the case where a strong Stackelberg equilibrium point is convenient for both firms. We first analyze the best-reply dynamics of the Stackelberg duopoly model such that each firm’s best-reply strategies set agree with the set of maximizers of the opponents’ strategies. Then, the classical Stackelberg duopoly game is transformed into a potential game in terms of the Lyapunov theory. As a result, a duopoly model has the benefit that the best-reply dynamics results in a natural implementation of the behavior of a Lyapunov-like function. In addition, the strong equilibrium point properties of Stackelberg and Lyapunov meet in potential games. We validate the proposed method theoretically by computing the complexity and by a numerical experiment related to the duopoly model.

Keywords: Dynamic duopoly model; complexity; strong Stackelberg equilibrium; Lyapunov equilibrium; Stackelberg games; Lyapunov games; Markov decision process (search for similar items in EconPapers)
JEL-codes: C32 C72 C73 D43 E37 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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