Admission control and pricing in a queue with batch arrivals

We investigate a problem of admission control in a queue with batch arrivals. We consider a single server with exponential service times and a compound Poisson arrival process. Each arriving batch computes its expected benefit and decides whether or not to enter the system. The controller’s problem is to set state dependent prices for arriving batches. Once prices have been set we formulate the admission control problem, derive properties of the value function, and obtain the optimal admission policy.     

A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains

Vertical cooperative (co-op) advertising is a marketing strategy in which the retailer runs local advertising and the manufacturer pays for a portion of its entire costs. This paper considers vertical co-op advertising along with pricing decisions in a supply chain; this consists of one manufacturer and one retailer where demand is influenced by both price and advertisement. Four game-theoretic models are established in order to study the effect of supply chain power balance on the optimal decisions of supply chain members. Comparisons and insights are developed. These embrace three non-cooperative games including Nash, Stackelberg-manufacturer and Stackelberg-retailer, and one cooperative game. In the latter case, both the manufacturer and the retailer reach the highest profit level; subsequently, the feasibility of bargaining game is discussed in a bid to determine a scheme to share the extra joint profit.     

A cooperative differential game model based on transmission rate in wireless networks

Network throughput and energy efficiency are paramount for network performance in an energy-constrained wireless network. However, it is difficult to achieve optimal objectives simultaneously. Therefore, it is necessary to find a rate control solution based on tradeoff between network throughput and energy efficiency. In this paper, we propose a cooperative differential game model and find an optimal rate control of each player to get the total minimal cost with tradeoff between network throughput and energy efficiency of the networks.     

A dynamic model for advertising and pricing competition between national and store brands

We study the relationship between the pricing and advertising decisions in a channel where a national brand is competing with a private label. We consider a differential game that incorporates the carryover effects of brand advertising over time for both the manufacturer and the retailer and we account for the complementary and competitive roles of advertising. Analysis of the obtained equilibrium Markov strategies shows that the relationship between advertising and pricing decisions in the channel depends mainly on the nature of the advertising effects. In particular, the manufacturer reacts to higher competitive retailer’s advertising levels by offering price concessions and limiting his advertising expenditures. The retailer’s optimal reaction to competitive advertising effects in the channel depends on two factors: (1) the price competition level between the store and the national brands and (2) the strength of the competitive advertising effects. For example, in case of intense price competition between the two brands combined with a strong manufacturer’s competitive advertising effect, the retailer should lower both the store and the national brands’ prices as a reaction to higher manufacturer’s advertising levels. For the retailer, the main advantage from boosting his competitive advertising investments seems to be driven by increased revenues from the private label. The retailer should however limit his investments in advertising if the latter generates considerable competitive effects on the national brand’s sales.     

Service rate control of closed Jackson networks from game theoretic perspective

Game theoretic analysis of queueing systems is an important research direction of queueing theory. In this paper, we study the service rate control problem of closed Jackson networks from a game theoretic perspective. The payoff function consists of a holding cost and an operating cost. Each server optimizes its service rate control strategy to maximize its own average payoff. We formulate this problem as a non-cooperative stochastic game with multiple players. By utilizing the problem structure of closed Jackson networks, we derive a difference equation which quantifies the performance difference under any two different strategies. We prove that no matter what strategies the other servers adopt, the best response of a server is to choose its service rates on the boundary. Thus, we can limit the search of equilibrium strategy profiles from a multidimensional continuous polyhedron to the set of its vertex. We further develop an iterative algorithm to find the Nash equilibrium. Moreover, we derive the social optimum of this problem, which is compared with the equilibrium using the price of anarchy. The bounds of the price of anarchy of this problem are also obtained. Finally, simulation experiments are conducted to demonstrate the main idea of this paper.     

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.     

A competitive dynamic pricing model when demand is interdependent over time

In this study, we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels. Customers can purchase and store the products, even if they do not need them at the time, in order to use them in future. The stockpile of the products generated by customers affects the demand in future periods. Therefore, the demand for each product not only is a function of prices and quality levels, but also of the products’ stockpile levels. In addition, the stockpile levels change the customers’ consumption behavior; more product in a stockpile leads to more consumption. Therefore, we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment.     

Product-design and pricing strategies with remanufacturing

In this paper, we consider a supply chain that consists of an original equipment manufacturer (OEM) producing new products and a remanufacturer recovering the used items. The OEM often faces a strategic dilemma when determining the degree of disassemblability of its product design, as high disassemblability decreases the OEM’s production costs as well as the remanufacturer’s recovery costs. However, high disassemblability may be harmful to the OEM in a market in which the remanufacturer is encouraged to intensify price competition with the OEM because design for high disassemblability leads to larger cost savings in remanufacturing. We first formulate a two-period model to investigate the OEM’s product-design strategy and the remanufacturer’s pricing strategy in an extensive-form game, in which the equilibrium decisions of the resulting scenarios are derived. Next, we show the thresholds that determine whether remanufacturing is constrained by collection, the thresholds for the remanufacturer’s choice of a profitable pricing strategy, and the thresholds for determining the OEM’s product-design strategy. Finally, we expand the model for a multiple-period problem to show that the main insights obtained from the two-period model can be applied.     

Mathematical structure of a bilevel strategic pricing model

This paper is concerned with the characterization of optimal strategies for a service firm acting in an oligopolistic environment. The decision problem is formulated as a leader–follower game played on a transportation network, where the leader firm selects a revenue-maximizing price schedule that takes explicitly into account the rational behavior of the customers. In the context of our analysis, the follower’s problem is associated with a competitive network market involving non atomic customer groups. The resulting bilevel model can therefore be viewed as a model of product differentiation subject to structural network constraints.     

A game theoretical approach to sharing penalties and rewards in projects

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary nondecreasing reward and penalty functions on the total expedition and delay, respectively. Attention is focused on how to divide the total reward (penalty) among the activities: the core of a corresponding cooperative project game determines a set of stable allocations of the total reward (penalty). In the definition of project games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of the reward (penalty) function at hand. It turns out that project games are related to bankruptcy and taxation games. This relation allows us to establish nonemptiness of the core of project games.     

Nash equilibria in all-optical networks

We consider the problem of routing a number of communication requests in WDM (wavelength division multiplexing) all-optical networks from the standpoint of game theory. If we view each routing request (pair of source-target nodes) as a player, then a strategy consists of a path from the source to the target and a frequency (color). To reflect the restriction that two requests must not use the same frequency on the same edge, conflicting strategies are assigned a prohibitively high cost.Under this formulation, we consider several natural cost functions, each one reflecting a different aspect of restriction in the available bandwidth. For each cost function we examine the problem of the existence of pure Nash equilibria, the complexity of recognizing and computing them and finally, the problem in which we are given a Nash equilibrium and we are asked to find a better one in the sense that the total bandwidth used is less. As it turns out some of these problems are tractable and others are NP-hard.     

An overview of Stackelberg pricing in networks

The Stackelberg pricing problem has two levels of decision making: tariff setting by an operator, and then selection of the cheapest alternative by customers. In the network version, an operator determines tariffs on a subset of the arcs that he owns. Customers, who wish to connect two vertices with a path of a certain capacity, select the cheapest path. The revenue for the operator is determined by the tariff and the amount of usage of his arcs. The most natural model for the problem is a (bilinear) bilevel program, where the upper level problem is the pricing problem of the operator, and the lower level problem is a shortest path problem for each of the customers.     

Modeling and optimization of energy efficient routing in wireless sensor networks

Wireless sensor networks (WSNs) have important applications in remote environmental monitoring and target tracking. The development of WSNs in recent years has been facilitated by the availability of sensors that are smaller, less expensive, and more intelligent. The design of a WSN depends significantly on its desired applications and must take into account factors such as the environment, the design objectives of the application, the associated costs, the necessary hardware, and any applicable system constraints. In this study, we propose mathematical models for a routing protocol (network design) under particular resource restrictions within a wireless sensor network. We consider two types of constraints: the distance between the linking sensors and the energy used by the sensors. The proposed models aim to identify energy-efficient paths that minimize the energy consumption of the network from the source sensor to the base station. The computational results show that the presented models can be used efficiently and applied to other network design contexts with resource restrictions (e.g., to multi-level supply chain networks).     

Location of terror response facilities: A game between state and terrorist

We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.     

Exact and heuristic methods to maximize network lifetime in wireless sensor networks with adjustable sensing ranges

Wireless sensor networks involve many different real-world contexts, such as monitoring and control tasks for traffic, surveillance, military and environmental applications, among others. Usually, these applications consider the use of a large number of low-cost sensing devices to monitor the activities occurring in a certain set of target locations. We want to individuate a set of covers (that is, subsets of sensors that can cover the whole set of targets) and appropriate activation times for each of them in order to maximize the total amount of time in which the monitoring activity can be performed (network lifetime), under the constraint given by the limited power of the battery contained in each sensor. A variant of this problem considers that each sensor can be activated in a certain number of alternative power levels, which determine different sensing ranges and power consumptions. We present some heuristic approaches and an exact approach based on the column generation technique. An extensive experimental phase proves the advantage in terms of solution quality of using adjustable sensing ranges with respect to the classical single range scheme.     

Control and voting power in corporate networks: Concepts and computational aspects

This paper proposes to rely on power indices to measure the amount of control held by individual shareholders in corporate networks. The value of the indices is determined by a complex voting game viewed as the composition of interlocked weighted majority games; the compound game reflects the structure of shareholdings. The paper describes an integrated algorithmic approach which allows to deal efficiently with the complexity of computing power indices in shareholding networks, irrespective of their size or structure. In particular, the approach explicitly accounts for the presence of float and of cyclic shareholding relationships. It has been successfully applied to the analysis of real-world financial networks.     

Optimal threshold policies in a two-class preemptive priority queue with admission and termination control

We consider a two-class 1 preemptive priority queue in which there are two essential, on-line decisions that have to be taken. The first is the decision to either accept or reject new type-1 or type-2 jobs. The second is the decision to abort jobs, i.e., to remove any type-1 or type-2 jobs from the system. We show that there exist optimal threshold policies for these two types of, decisions.