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Zbl 1237.91168
Fan, Yueqian; Xie, Tao; Du, Jianguo
Complex dynamics of duopoly game with heterogeneous players: a further analysis of the output model. (English)
[J] Appl. Math. Comput. 218, No. 15, 7829-7838 (2012). ISSN 0096-3003

Summary: In this paper, an output duopoly game with heterogeneous players is analyzed in order to study the influence of players' different behavior on the dynamics of game. Two types of players are considered, which are bounded rationality expectation and na{\"\i}ve expectation. Player with na{\"\i}ve expectation chooses an output level based on the market price of previous period, while player with bounded rationality adjusts his output adaptively, following a bounded rationality adjustment process based on a local estimate of the marginal profit of previous period. The game model is also based on the assumption that demand and cost function are nonlinear. The existence of equilibrium points and its local stability of the output game are investigated. The complex dynamics, bifurcations and chaos are displayed by numerical experiment. Numerical methods also show that the long-run average profit achieved by player adopting na{\"\i}ve expectation is higher than that achieved by player using self adaptive adjustment measure, although players use similar production methods.

MSC 2000:: *91B69
91B55
91A25 Dynamic games

Keywords: na{\"\i}ve expectation; bounded rationality; complex dynamics; heterogeneous expectation; long-run average profit

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