TY - JOUR
T1 - Analyzing an optimistic attitude for the leader firm in duopoly models
T2 - A strong stackelberg equilibrium based on a lyapunov game theory approach
AU - Clempner, Julio B.
AU - Poznyak, Alexander S.
N1 - Publisher Copyright:
© 2016, Bucharest University of Economic Studies. All rights reserved.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Complexity
KW - Dynamic duopoly model
KW - Lyapunov equilibrium
KW - Lyapunov games
KW - Markov decision process
KW - Stackelberg games
KW - Strong stackelberg equilibrium
UR - http://www.scopus.com/inward/record.url?scp=85034980955&partnerID=8YFLogxK
M3 - Artículo
SN - 0424-267X
VL - 50
SP - 41
EP - 60
JO - Economic Computation and Economic Cybernetics Studies and Research
JF - Economic Computation and Economic Cybernetics Studies and Research
IS - 4
ER -