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Abstract
Considering that the real competitions in service market contain two important factors, price and service, we build a dynamical price and service game model and study the complex dynamics of this bivariate game. Some special properties about the adjustment of service are noted by comparing our innovative bivariate game model with previous univariate game model. Besides, we discuss the stabilities of fixed points and compare the price and service game with price game. What is more, the recursive least-squares (RLS) estimation is introduced to substitute naive estimation; then the impacts of RLS estimation are studied by comparing it with naive estimation.
Highlights
Over the past several decades, bounded rational players’ dynamical competitions have attracted quite some attention
The evolution characteristics of system under recursive least-squares (RLS) estimation have been studied by [4, 21], but they did not investigate the difference between RLS estimation and naive estimation; in this paper, we study the difference between RLS estimation and naive estimation by comparing their stable regions, basin of attractions, and profits
We can know that price and service game will reduce the stable region of price adjustment parameter but can delay the appearance of chaos compared with price game; what is more, if the initial service is its equilibrium value, which one can bring more profit depends on the value of price adjustment parameter
Summary
Over the past several decades, bounded rational players’ dynamical competitions have attracted quite some attention. Dubovik and Janssen [16] considered an oligopolistic market where firms compete in price and quality and consumers are Mathematical Problems in Engineering heterogeneous in their knowledge of the prices and quality of products; they derived a perfect indicator equilibrium for this setting In these papers mentioned above, price, quality, and other variables (if exist), as decision variables, are endogenously chosen by firms. As far as we know, the analysis of the dynamical competition with both bounded rational players and multidecision variables is rare To fill this gap, in this paper we build a bivariate (price and quality of service) game model based on the fact that price and quality of service are the most vital factors in service market.
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