有限理性行为规则下豪泰林模型的复杂性

Complexity of the Hotelling model with bounded rationality rules

构建有限理性行为规则下的豪泰林(Hotelling)模型,分析参与人具有延迟反馈控制行为的豪泰林模型的复杂性.模型求解和数值模拟得出结论:在有限理性情况下,产品价格调整系数、产品位值和偏离成本等参数的取值范围决定了动态系统的稳定性、产量分岔、利润分岔和混沌;产品价格调整系数取值控制在适当范围,豪泰林均衡能够作为稳定的动态均衡实现.否则,即使企业实现了产品差异最大化豪泰林模型的均衡也可能不稳定,经济系统会出现周期变化和混沌现象;如果经济系统进入混沌状态,参与人对价格初值微小的调整都会引起价格发生巨大的波动;延迟反馈控制可以使处于混沌状态的系统转向均衡状态;同时论证了企业产品横向差异化可增加系统的稳定性.

This paper established a Hotelling model with bounded rationality, and analyzed the complexity of the dynamic system. By theory solution and numerical simulation we can get the conclusion that under bounded rationality, the coefficients of the price adjustment, the place, the deviation cost of the products and other parameter values determined the stability, the output bifurcation, profit bifurcation and chaotic state of the dynamic system. When the coefficients of price adjustment are in a proper range, Hotelling equilibrium can be realized as a stable dynamic equilibrium. Otherwise, the equilibrium will become unstable, bifurcation and chaos will occur to the economic system. If the economic system enters into chaotic state, a small variation in the initial value will cause a huge fluctuation of the price, then the market become unpredictable and the players can＇t make a reasonable decision of the future price; Delay feedback control can make the system from a chaotic state to a stable state. Demonstrated enterprises horizontal differentiation can increase the system stability.