In this paper, from the perspective of game theory, we study the impact of price subsidy and fairness concern on the pricing strategies and benefits of members in the take-away industry. In the single-channel supply chain, we build a Stackelberg game model between the take-away platform and the restaurant for the online take-away business. By comparing and analyzing the product pricing and revenue in the cases of no price subsidy and price subsidy, we obtain the optimal pricing strategy for both parties. In the dual-channel supply chain, we explore the benefits of supply chain members under the combined effects of fairness concern and price subsidy. Under the single channel price subsidy model, we find that restaurant always raises prices, and the price increase is directly proportional to the subsidy intensity. Such a proper price increase always brings more benefits to both parties. Under the dual-channel model, consumer fairness concern may curb the price increase behavior of restaurants. Regardless of the model, in the long term, the optimal subsidy of the platform will decrease with the expansion of the online take-away market.
We develop in this paper a new procedure to construct simultaneous confidence bands for derivatives of mean curves in functional data analysis. The technique involves polynomial splines that provide an approximation to the derivatives of the mean functions, the covariance functions and the associated eigenfunctions. We show that the proposed procedure has desirable statistical properties. In particular, we first show that the proposed estimators of derivatives of the mean curves are semiparametrically efficient. Second, we establish consistency results for derivatives of covariance functions and their eigenfunctions. Most importantly, we show that the proposed spline confidence bands are asymptotically efficient as if all random trajectories were observed with no error. Finally, the confidence band procedure is illustrated through numerical simulation studies and a real life example. 相似文献