Discrete Dynamics in Nature and Society

The uncertainty caused by emergencies will influence the normal operation of the supply chain. Considering demand disruptions, a closed-loop supply chain consisting of one manufacturer and two competing retailers based on decentralized decision-making is considered. In the supply chain, one retailer recovers end-of-life products while the other does not. Analytic results show that, when the disturbance of demand occurs, the manufacturer and retailers adjust the wholesale price and retail prices of products according to the direction of the market demand disruptions. Under demand disruptions, the retailer who participates in recovering can gain more profits, especially in the case of the positive disruption. Theoretic and pragmatic references for the emergency decision-making of closed-loop supply chain enterprises are provided.

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The idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analysis and generate new ideas to the state control measures. Keeping this in mind, using the strategies of IPM, we develop a prey-predator system with action threshold depending on the pest density and its change rate, and study its dynamical behavior. We develop new criteria guaranteeing the existence, uniqueness, local and global stability of order-1 periodic solutions. Applying the properties of Lambert function, the Poincaré map is portrayed for the exact phase set, which is helpful to provide the sufficient conditions for the existence and stability of the interior order-1 periodic solutions and boundary order-1 periodic solution, also confirmed by numerical simulations. It is studied in detail that how and under what conditions the fixed point of Poincaré map and its stability are affected by the newly introduced action threshold. The analytical methods developed in this paper will be very beneficial to study other generalized models with state-dependent feedback control.

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This paper investigates a dual exclusive channel model in which each manufacturer distributes its goods through a single exclusive retailer, but two goods are substitute. The decision rule between two channels is Nash game in Case 1, while it is Stackelberg game in Case 2. From manufacturer Stackelberg (MS), retailer Stackelberg (RS), and Nash game (VN) theoretic perspectives, nine game models are developed to examine the effect of product substitutability and relative channel status on pricing decisions at both horizontal competition and vertical competition levels. The analysis suggests that the type of price leadership scenarios, the level of product substitutability, and the relative channel status play a significant role in decision making. For instance, in case 1, the symmetric leadership (two manufacturers or two retailers are leaders) is always the dominant strategy and equilibrium for either two manufacturers or two retailers regardless of product substitutability and relative channel status. Nevertheless, the asymmetric leadership may lead channel members to encounter a prisoner’s dilemma if the relative channel status is small. By contrast, in Case 2, the symmetric leadership is not the unique dominant strategy for either two manufacturers or two retailers. In contrast to many earlier results, we also show that whether the first-mover and the late-mover advantages exist, depending on the level of related channel status.

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In some queueing systems, customers are frequently asked for giving a service quality feedback for their service at their service completion instants. Based on this phenomenon, in this paper, we model this type of queueing systems as clearing queues with service quality feedback and system maintenance. Once the system receives an unsatisfied (negative) feedback from customers (i.e., a customer is unsatisfied with the service), the system undergoes an adjustment procedure, and at the same time, all the present customers are forced to leave the system. By considering the waiting cost and reward, we discuss the joining behavior of customers and, respectively, derive the corresponding equilibrium joining strategies and social optimal strategies under different levels of information (the observable and the unobservable cases). Finally, some numerical examples are provided to show the effect of several system parameters on the equilibrium and optimal balking strategies.

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Institutional and individual investors are the two important players in the stock market. Together, they determine the price of the stock market. In this paper, an evolutionary game model that contains the two groups of players is proposed to analyze the stock price synchronicity considering the impacts of investors’ decisions on stock investment. Factors affecting investors’ decisions include the potential revenue or loss, the probability of gain or loss, and the cost of corresponding behavior. The proposed game model is analyzed by replicator dynamics equations and simulation of the evolutionary equilibrium strategy under different circumstances. The analysis shows that the operating cost of institutional investors, the cost of information collection before trading, and the expected loss that may be punished by regulators are the key factors that affect the evolutionary game system between institutional investors and individual investors. In addition, reducing the speculation in the market and increasing the information access of investors through the serious operation mode of institutional investors and the strengthening of the market information disclosure mechanism are beneficial to alleviate price synchronicity in stock market.

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In the present paper, we derive analytical formulas for barrier and lookback options with underlying assets exposed to multiple defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. An original technique is developed to valuate the barrier and lookback options by first conditioning on the predefault and the afterdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with the default-free option model and exogenous counterparty default risk option model.

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