Stackelberg Leader-follower Game Research Articles

Pricing and advertising decisions in a dominant-retailer supply chain: A multi-follower bi-level programming approach

Pricing and advertising is one of the most important decisions in each supply chain especially in the competitive environment. In the previous studies, this is as a centralized decision. However, if each channel member makes its decision independently, the utility of all members is optimized. In such decentralized situations, the channel members may have different market power that they influence on the other members’ decisions. These issues can modeled through leader-follower Stackelberg game or bi-level programming. This study investigates coordination of pricing and cooperative advertising in a two-stage supply chain consisting of one dominant-retailer and multiple competitive manufactures which produce several perishable and substitutable products. This paper aims to determine pricing and cooperative advertising decisions expenditure as well as the amount of manufacturers’ production or retailer’s purchase such that utility of all members is met. Hence, the problem is modeled as a multi-follower bi-level programming problem. Since it is proved that the model is NP-hard, the proposed model is solved through simulated annealing. A numerical example is used to show the impact of demand’s variations on the members’ decisions.

Economic and Environmental Life Cycle Optimization of Noncooperative Supply Chains and Product Systems: Modeling Framework, Mixed-Integer Bilevel Fractional Programming Algorithm, and Shale Gas Application

In this work, we propose a general modeling framework for the economic and environmental life cycle optimization of supply chains and product systems with noncooperative stakeholders. This framework is based on the functional-unit-based life cycle optimization approach and the leader–follower Stackelberg game structure to capture the decentralized feature and noncooperative relationships between multiple stakeholders across the product life cycle. The leader enjoys the priority of decision-making to optimize both its own economic performance and the life cycle environmental performance of the supply chain or product system. After the observation of leader’s decisions, the follower takes actions correspondingly to optimize its own economic performance. The resulting problem is formulated as a mixed-integer bilevel fractional program to account for conflicting objectives and interactions among different stakeholders. Design and operational decisions for both leader and follower are taken into consideration,...

Emerging Internet Content and Service Providers' Relationships: Models and Analyses of Engineering, Business and Policy Impact

We study engineering and business relationships between Content Providers and broadband access ISPs in various organizational and policy environments. We focus on pricing and capacity decisions for bandwidth and caches for delivery of the CP's content over the mile of the ISP's infrastructure. We model the CP-ISP interaction by the Stackelberg leader-follower game and the Integrated Operations model. We consider cases where premium bandwidth is offered to subscribers of the CP's service over the last mile, and cases where this is prohibited by Net Neutrality regulations. We develop a uniform solution procedure for all four resulting models. We explore the connections between optimal bandwidth and cache deployments, and, together with fees, their impact on the number of users, and related business and policy topics. We show that the decrease in profitability of caching due to Net Neutrality regulations is greater than the decrease from Integrated Operations to the Stackelberg game. In the Stackelberg game we prove that if a certain condition is satisfied, then with Net Neutrality the ISP will increase the cache price so that it is unprofitable for the CP to use caches. Moreover, this condition is satisfied in a typical case studied in detail.

Managing new and remanufactured products to mitigate environmental damage under emissions regulation

Emissions of greenhouse gases are not as free as they used to be. Under stringent regulations, manufacturers increasingly find that their emissions have a steep monetary, environmental and social price. In manufacturing industry, remanufacturing has an important role to play with its inherent economic, environmental and social opportunities which warrant regulatory action. In this paper, we characterize the optimal emissions taxation policy in order for remanufacturing to deliver those benefits. In particular, using a leader-follower Stackelberg game model, we investigate the impact of emissions taxes on the optimal production and pricing decisions of a manufacturer who could remanufacture its own product. We characterize whether/under what conditions the manufacturer’s decision to remanufacture under emissions regulation reduces its environmental impact (as measured by total greenhouse emissions), whilst increasing its profits (a win-win situation). On the policy side, we delineate how emissions taxes can be instituted to realize the inherent economic, environmental and social benefits of remanufacturing (the triple win of remanufacturing). Two critical components of this analysis are the issue of demand cannibalization from the remanufactured product and the low-emission advantage of remanufacturing. We further investigate the impact of remanufacturing- and society-related factors on the balance among firm-level profits, environmental impact and social welfare, where the collection rate of end-of-use products and the cost to the environment turn out to be decisive in deriving the triple win benefits from remanufacturing. Last, we extend our analyses to an emissions trading setting where emissions are regulated using tradeable permits, and investigate the economic implications of remanufacturing under emissions trading vis-á-vis emissions taxation.

Modeling the multi-traffic signal-control synchronization: A Markov chains game theory approach

This paper presents a new paradigm for modeling the multi-traffic signal-control synchronization problem using game theory based on the extraproximal method. The objective in a crossing is to minimize the queuing delay and the problem for a signal controller is to find an optimal signal timing strategy, i.e. establishing green timing for each signal phase. Signal controllers are considered the players of the game. Each intersection aims at finding the green time that minimizes its signal and queuing delay. The problem presents natural restrictions: (a) the number of entering cars and exiting cars is different for each street of the intersection and (b) the interval of time given for vehicles to the green light is equal to the red light in the respective opposite direction . The first restriction determines a leader–follower Stackelberg game model: streets having more traffic require more green time. The last restriction establishes a simultaneous-solution of the game as a better consideration of the real situation. Then, to take advantage of the structure of the game, the paper shows that the solution is given by a Nash equilibrium. We introduce the c-variable method for finding the optimal signal timing distribution and making the problem computationally tractable. The extraproximal method is a two-step iterated procedure: (a) the first step calculates a preliminary approximation to the equilibrium point, and (b) the second step is designed to find an adjustment of the previous step. The formulation of the game is given in terms of coupled nonlinear programming problems implementing the Lagrange principle. Tikhonov׳s regularization method is employed to ensure the convergence of the costfunctions to a Nash equilibrium point. In addition, the extraproximal method is developed in terms of Markov chains. The usefulness of the method is demonstrated by a three-way intersection example. The contributions have major implications for real-world applications.

Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game

Product family design by module configuration is conducive to accommodating product variety while maintaining mass production efficiency. Effective fulfillment of product families necessitates joint decision making of product family configuration (PFC) and downstream supply chain configuration (SCC), due to nowadays manufacturers’ moving towards assembly-to-order production throughout a distributed supply chain network. Existing decision models for joint optimization of product family and supply chain configuration are originated from an “all-in-one” approach that assumes both PFC and SCC decisions can be integrated into one optimization problem by aggregating two different types of objectives into a single objective function. Such an assumption neglects the complex tradeoffs underlying two different decision making problems and fails to reveal the inherent coupling of PFC and SCC.This paper formulates joint configuration of a product family and its supply chain as a leader-follower Stackelberg game that is enacted through a bi-level hierarchical optimization mechanism to model the coordination between two self-interested decision makers for PFC and SCC. The PFC decisions are modeled as an upper-level optimization problem (called leader) for optimal selection of modules, module instances, and product variants. The SCC decisions are modeled as a lower-level optimization problem (called follower), which responds to decisions of the upper level in order to determine an optimal supply chain configuration and inventory policies. A nonlinear, mixed integer programming model is formulated for the bi-level joint decision in the leader-follower game. To solve the nonlinear optimization model, a bi-level, nested genetic algorithm with constraint reasoning is developed and implemented. A case study of a power transformer product family and supply chain configuration is reported to demonstrate the feasibility and potential of the proposed leader-follower game-theoretic method.

Research on Supply Chain Profit Coordination Mechanism Based on JIT Lot-Splitting

A supply chain profit coordination mechanism based on JIT lot-splitting, which involves a two stage supply chain consisted of a supplier and a buyer, is discussed. Based on the bargaining power of supplier, the profit coordination with and without incentives are respectively explored. For the total cost minimizations of buyer and supplier separately, two stage stackelberg leader-follower game models, in which buyer is the leader and supplier is the follower, are established. Supplier applies JIT delivery to reduce buyer’s cost and the total cost of the supply chain via dividing buyer’s order per batch into some batches to deliver. Finally, a numerical example and a simulation analysis are given and the impact of the variation of relative parameters on the total cost saving of buyer, supplier and system is discussed. In addition, the efficiency of game decision on the basis of JIT lot-splitting is proved.

Deal or No Deal?: Advertizing and Sampling Effects on Two-Sided Daily Deal Platforms

With the advent of Groupon.com in 2008, daily deal platforms have seen phenomenal growth. But surprisingly there is very sparse analytical research that has studied the economics of daily deal platforms which are two-sided in the sense that they connect merchants on the one side to consumers on the other side. We develop a stylized two-period game-theoretic model to analyze the strategic interaction between heterogeneous merchants and consumers. In our conceptualization, a monopolist daily deal platform is revenue maximizer who not only takes into consideration the cross-side network effect leading to chicken-and-egg problem, but also sampling and advertizing effect due to the presence of the platform. Keeping in view the realworld market conditions, we do not impose the restriction that the two-sides can interact only through the platform and allow the two-sides to transact outside the platform too. We model the strategic interaction between the daily deal website (platform) and merchants as a Stackelberg leader-follower game where merchants choose discount rate, keeping that in view the platform’s choice of the fixed fee rate or revenue sharing rate. Our result shows the merchants offer higher discount rate on the daily deal website than outside the website, and surprisingly, merchants’ optimal choice of discount rate is independent from the platform’s fixed fee rate. We also show that merchants that are new in the market place and therefore, less well-known gain more from offering a deal on the daily deal website. Some of merchants never offer a deal on the platform even if offering a deal on the platform is free.

TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems Using Game Theory

In proof‐of‐payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of fare evasion depends on the unpredictability and effectiveness of the patrols. In this article, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader‐follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism‐motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to execute. We present an efficient algorithm for computing such patrol strategies and present experimental results using real‐world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff's Department is currently carrying out trials of TRUSTS.

Crude Oil Market Power—A Shift in Recent Years?

We investigate the exertion of market power in the global crude oil market over the past years. Recognizing the difficulty of identifying market power in the crude oil market by empirical studies, we propose a numerical partial equilibrium model formulated as a mixed complementarity problem. Our approach allows for strategic behavior in a Nash-Cournot market, a Stackelberg leader-follower game, an OPEC oligopoly or cartel, as well as perfect competition. To take account of liquid spot markets, the model specifically includes arbitragers to capture the effect of global crude oil market integration. Our results indicate a market structure shift over the past years. Reported quantities and prices before the 2008 turmoil are close to those derived from a Stackelberg market simulation, with Saudi Arabia acting as Stackelberg leader vis-a-vis a non-cooperative OPEC oligopoly and a competitive fringe. However, in 2008 and 2009, observed prices are closer to the competitive benchmark. We conclude that OPEC suppliers’ ability to exert market power was reduced in the 2008 turmoil and its aftermath.

TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of such fines depends on the unpredictability and effectiveness of the patrols. In this paper, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to be executed. We present an efficient algorithm for computing such patrol strategies and present experimental results using real-world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff’s department has begun trials of TRUSTS.

Biofuel supply chain design under competitive agricultural land use and feedstock market equilibrium

The rapid expansion of the biofuel industry diverts a large amount of agricultural crops as energy feedstocks, and in turn affects farm land allocation, feedstock market equilibrium, and agricultural economic development in local areas. In this paper, we propose game-theoretic models that incorporate farmers' decisions on land use and market choice into the biofuel manufacturers' supply chain design problem. A noncooperative bi-level Stackelberg leader–follower game model and a cooperative game model are developed respectively to address possible business partnership scenarios between feedstock suppliers and biofuel manufacturers. The models determine the optimal number and locations of biorefineries, the required prices for these refineries to compete for feedstock resources, as well as farmers' land use choices between food and energy. Using corn as an example of feedstock crops, spatial market equilibrium is utilized to model the relationship between corn supply and demand, and the associated price variations in local grain markets. With linear corn demand functions, we develop a solution approach that transforms the original discrete mathematical program with equilibrium constraints (DC-MPEC) into to a solvable mixed integer quadratic programming (MIQP) problem based on Karush–Kuhn–Tucker (KKT) conditions. The proposed methodology is illustrated using an empirical case study of the Illinois State. The computation results reveal interesting insights into optimal land use strategies and supply chain design for the emerging “biofuel economy”.

Supply Chain Coordination Mechanism Based on Lead-Time Compression under Elastic Demand

The optimization for profit coordination of the supply chain under elastic demand, which involves a two-level supply chain consisted of a supplier and a buyer, is discussed. Supplier supplies in JIT mode and supply chain members reduce lead-time through lead-time crashing to reduce costs. Based on game theory and the aim of minimizing the total cost of each party respectively, a two-level stackelberg leader-follower game model, in which buyer is the leader and supplier is the follower, is established. Buyer takes all the crashing cost and gives incentives to supplier to promote cooperation. A comparison is given among the profits of buyer, supplier and system after and not after lead-time crashing respectively, and the increased benefit among the three parties after lead-time crashing is analyzed, too. Finally, a numerical example and a simulation analysis are given to show the effect of the variations of the parameters on the increased benefit of buyer, supplier and system.

Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness

There has been significant recent interest in game-theoretic approaches to security, with much of the recent research focused on utilizing the leader-follower Stackelberg game model. Among the major applications are the ARMOR program deployed at LAX Airport and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackelberg games is that security forces (leaders), acting first, commit to a randomized strategy; while their adversaries (followers) choose their best response after surveillance of this randomized strategy. Yet, in many situations, a leader may face uncertainty about the follower’s surveillance capability. Previous work fails to address how a leader should compute her strategy given such uncertainty. We provide five contributions in the context of a general class of security games. First, we show that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, under a natural restriction on security games, any Stackelberg strategy is also a Nash equilibrium strategy; and furthermore, the solution is unique in a class of security games of which ARMOR is a key exemplar. Third, when faced with a follower that can attack multiple targets, many of these properties no longer hold. Fourth, we show experimentally that in most (but not all) games where the restriction does not hold, the Stackelberg strategy is still a Nash equilibrium strategy, but this is no longer true when the attacker can attack multiple targets. Finally, as a possible direction for future research, we propose an extensive-form game model that makes the defender’s uncertainty about the attacker’s ability to observe explicit.

Supply Chain Revenue Coordination Mechanism Based on Game and Lead Time Compression with 3PL Intervention

A revenue coordination problem of supply chain based on lead time compression is discussed. The coordination problem involves in a supply chain consisted of a manufacturer, a third-party logistics and a vendor. The vendor implements a lot-partitioning supply model. The third-party logistics undertakes the delivery. The supply chain gains Lead time compression with lead time crashing. According to different cooperative modes, Stackelberg leader-follower game models are established to gain the optimal costs of the buyer, the vendor and the supply chain system. A decision principle is designed to compare the cost savings of the buyer, the vendor, the third-party logistics and the system. A best mode is singled out according to the decision principle.

Real Options Games in Complete and Incomplete Markets with Several Decision Makers

We consider optimal investment policies for irreversible capital investment projects under uncertainty in a monopoly situation and in a Stackelberg leader-follower game. We consider two types of payoffs: lump-sum and cash flows. The decisions are the times to enter into the market. The problems belong to the class of optimal stopping times, for which the right approach is that of variational inequalities (V.I.s). In the case of complete markets, payoffs are expected values with respect to the risk-neutral probability. In the case of incomplete markets, the risk-neutral probability is not defined. We consider an investor maximizing his/her utility function, and we consider the investment in the project as an additional decision, besides portfolio investment and consumption decisions. This decision remains a stopping time, conversely to the portfolio investment and consumption decisions (continuous controls). The game problem raises new difficulties. The leader's V.I. has a nondifferentiable obstacle. The weak formulation of the V.I. handles this difficulty. In some cases, the solution of the V.I. may be continuously differentiable although the obstacle is not. An additional difficulty occurs for lump-sum payoffs in the case of incomplete markets. We cannot compare gains and losses at different times. We propose an alternative approach, using equivalence (indifference) considerations. In the case of payoffs characterized by cash flows, this difficulty does not exist, but an intermediary problem arises which has a nice interpretation as a differential game. The solutions thus obtained for the Stackelberg game are not intuitive. Therefore, competition has important consequences on investment decisions.

WIRELESS BROADBAND ACCESS: WIMAX AND BEYOND - Integration of WiMAX and WiFi: Optimal Pricing for Bandwidth Sharing

Broadband wireless access networks based on WiMAX can provide backhaul support for mobile WiFi hotspots. We consider an integrated WiMAX/WiFi network for such an application where the licensed WiMAX spectrum is shared by the WiFi access points/routers to provide Internet connectivity to mobile WiFi users. The WiMAX backbone network and WiFi hotspots are operated by different service providers. Issues such as protocol adaptation, quality of service support, and pricing for bandwidth sharing that are related to integration of these networks are discussed. In addition, we propose a model for optimal pricing for bandwidth sharing in an integrated WiMAX/WiFi network. A Stackelberg leader-follower game is formulated to obtain the optimal pricing solution for bandwidth sharing. Performance evaluation results reveal some interesting insights into the problem

Leader–follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices

Vendor-managed inventory (VMI) is a widely used co-operative inventory policy in supply chains in which each enterprise has its autonomy in pricing. In this paper, a leader–follower Stackelberg game in a VMI supply chain is discussed where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market-related parameters on the profits of the manufacturer and its retailers. Through a numerical example, our research demonstrates that: (a) the market-related parameters have significant influence on the manufacturer's and its retailers' profits; (b) a retailer's profit may not necessarily be lowered when it is charged with a higher inventory cost by the manufacturer; and (c) the equilibrium of the Stackelberg equilibrium benefits the manufacturer.

An analysis of interorganizational resource sharing decisions in collaborative knowledge creation

Collaborative relationships between organizations for knowledge creation have received considerable attention in recent literature. For any collaborative endeavor to succeed, adequate allocation and sharing of resources is important. We explored the conditions of resource sharing in which organizations are motivated to collaborate for knowledge creation, as well as the conditions required for the collaboration to continue. Using the game theoretic framework, we modeled the collaboration for knowledge creation as a Stackelberg leader–follower game. Specifically, we modeled two scenarios, the first in which organizations expend current efforts only, and the second in which organizations have made relevant prior efforts. The equilibrium values of current efforts in knowledge creation, the leader organization’s resource participation rate, and the total expected system gain in both of these scenarios were determined. Both within scenario and cross-scenario analyses were conducted. It is important to maintain an optimal ratio between the leader’s and follower’s marginal gains for the formation and continuation of the collaboration.

Dynamic Game Theoretic Model of Multi-Layer Infrastructure Networks

Due to similarities in terms of network structure and interactions among them, most infrastructure systems can be viewed as coupled layers of a generalized transportation network in which the passenger, freight, data, water, and energy flows are the commodities in the different layers. The coupling is due to the varying degrees of interactions among these layers in terms of shared physical networks, budgetary constraints, socio-economic environments, environmental concerns, information/other resources, and in particular, functional interdependencies. However, these interactions are normally ignored in the engineering planning, design and analysis of infrastructure systems. Identifying and understanding these interactions using a holistic perspective can lead to more efficient infrastructure systems. This paper presents a preliminary network flow equilibrium model of dynamic multi-layer infrastructure networks in the form of a differential game involving two essential time scales. In particular, three coupled network layers—automobiles, urban freight and data—are modeled as being comprised of Cournot-Nash dynamic agents. An agent-based simulation solution structure is introduced to solve the flow equilibrium and optimal budget allocation problem for these three layers under the assumption of a super authority that oversees investments in the infrastructure of all three technologies and thereby creates a dynamic Stackelberg leader-follower game.