Stackelberg Leader Research Articles

Manufacturer encroachment and extended warranty provision

This study focused on the interactions between manufacturer encroachment and extended warranty (EW) provision by examining the manufacturer's optimal encroachment decision with or without the extended warranty and the optimal EW provision decision under encroachment or no encroachment. Based on the combination of the two strategies, this study discussed four different models in which the manufacturer and retailer act as the Stackelberg leader and follower, respectively. It was shown that the manufacturer always finds it optimal to offer EW without encroachment. However, under encroachment, the manufacturer's motivation to offer EW weakens. Furthermore, when EW is not offered, the manufacturer can benefit from encroachment if the selling cost of the product is not sufficiently high. When the selling cost of EW is low, the manufacturer's motivation for encroachment strengthens. As the selling cost becomes moderate to high, offering EW weakens the manufacturer's motivation for encroachment. Our analysis reveals that for different values of the co-payment rate and the manufacturer's selling costs of products and EW, encroachment and EW provision may reinforce or impair each other. Therefore, manufacturer has to pay attention to the influence of one decison on another decision.

Decision-making in low carbon supply chains: a blockchain-based lcsp perspective and a differential game model

Blockchain technology has reshaped how members of supply chains transfer information, effectively avoiding the phenomenon of information silos and helping to improve the emissions reduction performance and profit of each subject in the supply chain. It is now critical to understand how supply chain members can be encouraged to collaboratively invest in low-carbon service platforms based on blockchain technology to realise chain-wide systematic carbon reduction. In this regard, considering the time-dynamic characteristics of enterprise emissions reduction, this paper establishes a differential game model of collaborative emissions reduction in a low-carbon supply chain composed of a Stackelberg leader manufacturer and a supplier. We compare and analyse the four investment decision scenarios regarding whether the supplier and manufacturer invest in the blockchain low-carbon service platform under decentralised decision-making, as well as the equilibrium solutions of supply chain members under centralised decision-making scenarios by solving the Hamilton function. Finally, we introduce a bilateral cost-sharing contract to make the supply chain perfectly coordinated. We find that the significant unit return is an important incentive for supply chain members to take the lead in investing in a low carbon service platform (LCSP). In this regard, when only one member invests, the other one demonstrates free-riding behaviour. Under centralised decision-making, the supply chain can achieve Pareto optimality, and the bilateral cost-sharing contract can achieve perfect coordination of the supply chain, which is the best choice for the decision-makers of low-carbon supply chains. As the influence level of the LCSP gradually increases from small to large, the optimal decision-making of supply chain members gradually transitions from waiting for the right time to “hitchhike” to a strong willingness to cooperate. This study is of great reference value and practical significance for economic entities to improve profits, promote systematic carbon reduction in the whole chain and promote the sustainable development of low-carbon supply chains.

Optimal decision-making and coordination of the shipping logistics service supply chain cooperation mode under the carbon quota and trading mechanism

Carbon cap-and-trade policy based on market mechanism becomes an important means to restrain shipping logistics enterprises' carbon emission reduction. This paper studies the new requirements of shipping enterprises under the pressure of carbon emission reduction. Considering the logistics service supply chain composed of two competing providers and one integrator under the constraint of carbon cap-and-trade policy, this paper explores the optimal pricing and revenue decision of shipping logistics service supply chain through vertical cooperation, horizontal cooperation between providers and revenue sharing cooperation among integrators. This paper obtains feedback strategies under different cooperation modes by constructing a game model. In the vertical game, the shipping logistics supplier is the Stackelberg leader, and the shipping logistics integrator is the follower; there is a Nash equilibrium in the emission reduction decisions among suppliers in the horizontal game. On this basis, the results of different cooperation modes are compared, and the influence of competitive strategies on the optimal results is discussed. We found that the vertical cooperation of the shipping logistics service supply chain has a higher carbon emission reduction rate and a lower sales price, and the horizontal cooperation of shipping logistics suppliers can improve their own profits but reduce the income of the shipping logistics integrators and consumer welfare. When the revenue sharing contract provides the shipping logistics integrator with a share proportion in a certain range, the revenue sharing contract can generate higher supply chain profits than the integration of two chains, which can urge shipping logistics suppliers to forfeit the horizontal cooperation and help the shipping logistics service supply chain achieve win-win results.

Should Bank Provide Insurance for Horticultural Crop Damage? (A Stackelberg Game Approach)

Abstract This study provides insight for a bank to insure farmers with the possibility of having horticultural crops damaged. Specifically, a Stackelberg leadership game is formulated with the bank as the leader and the farmer as the follower. The bank declares its insurance fee first to anticipate the horticulture prices and maximize its profit. Then, the farmer decides the horticulture price sequentially given the insurance fee and the crop condition. The game is solved under the with and without insurance scenarios. The farmer decides its horticulture price with no banking insurance fee in without insurance scenario. The bank decision-making is only included in with insurance scenario. From the analytical comparison result, it is better for the farmer to have insurance from the bank when the probability of damage to a horticultural crop exists. However, the bank should give an insurance fee to the farmer with a high probability of having good horticultural crops and less customer sensitivity to damaged crops.

Recycling investment strategies in two‐sided competition with diverse vertical structures

AbstractThe supply chain consisting of an original equipment manufacturer (OEM) and a downstream retailer encounters vertical competition along with two‐sided competition from a third party remanufacturer (3PR). The two‐sided competition refers to competition in both recycling and sales. We investigate the recycling investments by the OEM and retailer in diverse vertical structures. Our findings indicate that cooperative investment is optimal when either the OEM or retailer is the Stackelberg leader, but neither party is willing to invest in recycling when they are in vertical Nash. The experiments reveal that the OEM, acting as the Stackelberg leader, and implementing the cooperative investment strategy, yields better economic and environmental benefits.

Retracted: On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

Retracted: On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

Pioneering paradigms: unraveling niche opportunities in green finance through bibliometric analysis of nation brands and brand culture

<abstract><p>This study reviews the literature focused on nation brands and brand culture through the innovative combination of latent Dirichlet allocation with a multinomial and unordered discrete choice analysis. Unlike a narrow perspective of bibliometric work, which confines itself to reviewing existing literature within a specific research domain, a broader viewpoint leverages bibliometric analysis to pinpoint potential research opportunities indicative of emerging trends in related fields. Adopting this comprehensive paradigm, the current study scrutinizes 60 articles spanning the timeframe from 1992 to 2021. The analysis discerns six prospective marketing strategies instrumental in propelling a country to global brand prominence: the synergistic integration of country-of-origin and city brands, consumption branding, materialistic branding, green branding, ideological branding, and scientific branding. Notably, environmental branding has assumed a pivotal global role post–2015, while ideological branding represents a more recent trend centered on diligent efforts to invigorate national identity systems. Empirical insights underscore the need of a multidisciplinary approach in the creation of nation brands, suggesting that distinct strategies need not be mutually exclusive. Quantitatively, it is found evidence that covering one additional environmental topic in a study increases (decreases) its likelihood of belonging to the consumption (ideology) cluster by 50.8 (50.6) percentage points, respectively. Strategic recommendations for future national endeavors emphasize the significance of becoming a Stackelberg leader in the race to generate added value. Collectively, these findings underscore that the bibliometric analysis employed to elucidate the evolution of nation brands and brand culture, typically associated with international marketing, unveils two promising niche areas for future research in green finance: <italic>green nation brands</italic> and <italic>green brand culture</italic>. The former pertains to asset allocations within green enterprises and environmental sectors, enhancing a country's symbolic commitment to the burgeoning green paradigm. Meanwhile, the later delves into the internalization of fintech development's growth and intermediary effects, fostering green innovation, energy efficiency, and green supply chains. This bottom-up approach is geared towards meeting community-based needs and presents valuable avenues for future exploration in the field of green finance.</p></abstract>

The Stackelberg vs. Nash-Cournot Folk-theorem in international environmental agreements

A commonly reported result in the literature on international environmental agreements (IEAs) is that if coalition members act as Stackelberg leaders (Stackelberg scenario) this leads to larger stable coalitions than if signatories act simultaneously with non-signatories (Nash-Cournot scenario). This result has been taken for granted, a kind of Folk-theorem, even though it has been proven at best for specific payoff functions, and very often the conclusion is only based on simulations. We prove the Stackelberg vs. Nash-Cournot Folk-theorem based on a generic payoff function for a public good provision game.

Pricing decisions in a two-period closed-loop supply chain game under asymmetric information and uncertainty

AbstractStrategies to increase sustainability are of growing relevance for supply chains and especially for the management of production processes. In this paper, we build on existing literature in closed-loop supply chain management and consider a two-period game-theoretic model in which product returns are reused in the manufacturing process. In all scenarios, we assume that the return rate of used products is random and not known to the players at the beginning of the planning horizon, thus, they have to deal with uncertainty in period 1. In contrast to existing literature, we will also address the circumstance that the players’ level of information in period 2, after the returns have been realized, can be linked to the collection mode in the supply chain. In Scenario A, the retailer is involved in the collection of the used products and transfers them to the manufacturer, so that symmetric information is available. In Scenario B, on the other hand, the used products reach the manufacturer directly from the customer, so that the manufacturer has an information advantage over the retailer. By comparing these scenarios and a vertically integrated supply chain benchmark case, it becomes clear that, depending on the actual return rate, the presence of private information can be either beneficial or detrimental to the manufacturer. The retailer, on the other hand, can compensate for information disadvantages in most cases over the multi-period planning period due to its position as a Stackelberg leader. Regardless of the amount of a transfer payment offered to it by the manufacturer, it prefers the collection of the goods by the manufacturer itself. These findings contribute to literature on symmetric information, where, for example, a retailer-led collection is preferred (Savaskan et al. Manage Sci 50(2):239–252, 2004) or the decision depends on the amount of the transfer payment (Modak et al. J Clean Prod 171:512–528, 2018). However, we show that cooperation between the players leads to the best results not only economically but also from an ecological point of view.

Nash-Bargaining Fairness Concerns under Push and Pull Supply Chains

Unbalanced power structures can lead to an inequitable distribution of the supply chain’s profits, creating unstable supply chain relationships and serious social problems. This paper builds a two-tier newsvendor model composed of a single supplier and a single retailer and introduces Nash bargaining as a reference for fairness. We investigate (1) the impact of fairness concerns on the performance of a retailer-dominated supply chain and a manufacturer-dominated supply chain; (2) how demand uncertainty affects the inequitable state; and (3) how overestimated and underestimated values of fairness concerns affect supply chain performance when fairness concerns are private information. After solving the equilibrium solution of the Stackelberg game and Nash-bargaining games and numerical analyses, it is shown that unilateral fairness concerns by the Stackelberg leader or follower can motivate the leader to sacrifice its profit to reduce their income inequality by offering a coordinating wholesale price. Of course, it is also effective for both participants to be fair-minded as soon as their fairness sensitivity is moderate enough. However, followers’ fairness concerns are more effective at decreasing inequity, while leaders can improve social welfare, i.e., increase the entire supply chain’s efficiency as well as market scale. We also find that in a more uncertain market, fewer fairness-concerned participants are supposed to reach a relatively fair condition. In addition, we conclude that sometimes asymmetric information about fairness concerns can improve the profit share of the disadvantaged and even channel efficiency. This paper extends the study of Nash-bargaining fairness concerns to retailer-dominated newsvendor models and enriches the field, when fairness concerns are asymmetric information.

A game theoretic approach to contract-based enviro-economic coordination of wood pellet supply chains for bioenergy production

Wood pellets have gained global attention due to their economic availability and increasing demand for bioenergy as part of sustainable energy solutions. Management of the wood pellet supply chains, from feedstock harvesting to bioenergy conversion, is critical to ensure competitiveness in the energy markets. In this regard, wood pellets supply chain coordination can play a strategic role in enhancing the efficiency and reliability of bioenergy generation. This study proposes a contract-based coordination mechanism for wood pellet supply chains and compares its performance in alternative centralized and decentralized decision-making structures. A bi-level nonlinear game-theoretic approach with two economic and environmental objective functions is developed. It utilizes the concept of life cycle assessment in a Stackelberg leader–follower game to obtain the bioenergy equilibrium solutions. Further, this study examines the case of wood pellet supply chains in three remote Canadian communities. The aim is to showcase the practicality and significance of the proposed approach and interpret the findings. By focusing on these communities, the crucial role of supply chain coordination in fostering sustainable development, particularly, in the context of bioenergy generation is emphasized. The study colludes by advocating a number of avenues for future research.

A game-theoretic approach to designing carbon regulations in a duopoly freight transportation market: Road and multimodal road-rail competitive systems.

Since the transportation industry produces remarkable carbon emissions worldwide, governments aim to curb these emissions by implementing different carbon regulations. However, little is known regarding how the heterogeneity of transportation systems should be exploited to design carbon regulations. To fill this research gap, the present article formulates carbon cap-and-trade and carbon offset regulations to reduce total carbon emissions produced by road and multimodal road-rail freight transportation systems (FTSs) in a duopoly market; the latter is regarded as a green, energy-efficient transportation mode. A novel procedure is suggested to allocate initial carbon caps that is a hybrid of both benchmark and grandfathering methods. The procedure allows the government to exploit the energy efficiency of the multimodal system, when targeting a reduction of total carbon. Then, a game-theoretic approach is adopted to implement the mentioned carbon regulations. A government, as a Stackelberg leader, maximizes a social welfare function containing economic, social, and environmental dimensions. Under the cap-and-trade regulation, a Nash bargaining process is proposed to trade carbon permits between the FTSs, as the followers, for updating their initial caps. The equilibrium outputs of the two mentioned carbon regulations and a carbon tax regulation are compared. The findings based on an experimental analysis suggest that the cap-and-trade (carbon offset) is the optimal and energy-efficient regulation from the social (economic or environmental) perspective. In terms of policy implications, our findings indicate that the development of a marketplace infrastructure for trading carbon permits is not justifiable under theeconomic and environmental perspectives of the government.

Premilinary analysis of cross-shareholding in the green supply chain and recommendations for regulatory policy in the Philippines

Cross-shareholding is increasingly used in supply chains to improve strategic synergy between companies. However, regulations on cross-ownership within green supply chains are still in their early stages of development. Cross-ownership affects both the government’s pricing strategy and its carbon reduction policies. Additionally, the cross-shareholding structure impacts the profitability of the supply chain by introducing power dynamics between manufacturers and retailers. When cross-shareholding regulations and models are implemented, manufacturers and retailers within the supply chain exhibit more substantial reductions in their carbon footprint and experience increased profits, particularly in decentralized supply chains when cross ownership surpasses a specific threshold. The adoption of cross-shareholding profit-sharing agreements could enhance the performance of green supply chains. This article synthesizes the views of scholars on cross shareholding in the supply chain. It uses analytical methods to evaluate the role of the negotiation process, trade credit, and cross-shareholding in the supply chain. The article uses jurisprudence to recommend a cross shareholding policy in the Philippines to enhance supply chain efficiency. It uses the “Stackelberg Leadership Model” to analyze the impact of cross-shareholding on two levels of the supply chain, offering recommendations for future implementation to improve supply chain efficiency. The article recommends that the Philippines’ supply chain policy include mechanisms to encourage new companies to join the existing cross-ownership network, capitalize on the impact of cross-shareholding on supply chain assessment, and develop ways to use equity ratio and trade credit. These recommendations aim to refine policy and legislation in the Philippines to effectively utilize trade credit, equity ratios, and cross-shareholdings in supply chain management.

Spying and imperfect commitment in first-price auctions: a case of tacit collusion

We analyze Stackelberg leadership in a first-price auction. Leadership is induced by an information system, represented by a spy, that leaks one bidder’s bid before others choose their bids. However, the leader may secretly revise his bid with some probability; therefore, the leaked bid is only an imperfect signal. Whereas leadership with perfect commitment exclusively benefits the follower, imperfect commitment yields a collusive outcome, even if the likelihood that the leader may revise his bid is arbitrarily small. This collusive impact shows up in all equilibria and is strongest in the unique pooling equilibrium which is also payoff dominant.

A Bilevel Model for Robust Network Design and Biomass Pricing Under Farmers’ Risk Attitudes and Supply Uncertainty

This paper addresses an integrated biomass pricing and logistics network design problem. A bilevel design and pricing model is proposed to capture the dynamic decision process between a biofuel producer as a Stackelberg leader and farmers as Stackelberg followers. The bilevel optimization model is transformed into a tractable single-level formulation by using optimality constraints. Other unique characteristics of our problem at hand include the incorporation of the harvesting time and frequency decisions in the biomass supply chain network design problem for the first time and consideration of the uncertainty in switchgrass yield in a robust optimization setting to take into account the risk-averse behavior of the farmers (suppliers). To efficiently solve the model, we propose a Benders decomposition algorithm enhanced by surrogate constraints, strengthened Benders cuts, and in-out cut loop stabilization. The numerical experiments show that the proposed algorithm is significantly superior to the branch-and-cut approach of CPLEX in terms of run times and gaps. We conduct a case study with data from Texas to validate the capabilities of our mathematical model and solution approach. Based on extensive experiments, the benefits of modeling are analyzed, and significant insights are explored. Funding: This research was partially supported by the National Natural Science Foundation of China [Grants 71771135, 72171129]; and the scholarship from China Scholarship Council (CSC) [Grant CSC 201906210092]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0357 .

Cooperative Jamming-Assisted Untrusted Relaying Based on Game Theory for Next-Generation Communication Systems

In this contribution, we investigate the performance of an untrusted relaying system when Cooperative Jammers (CJs) are available. We propose two scenarios, Untrusted Relaying-aided Multiple Cooperative-Jammers-based Simultaneous Transmission (UR-MCJST) and an Untrusted Relaying-aided Multiple Cooperative Jammers-based Time-Division Transmission (UR-MCJTDT). The performances of both UR-MCJST and UR-MCJTDT schemes are investigated. The source node is the primary user (PU) that has access to a transmission bandwidth. An untrusted relay is employed for improving the reliability of the PU transmission, while CJs are invoked for improving the secrecy rate of the PU transmission. The transmission strategy for the scheme proposed in this paper is split into three unique phases. The first phase is called the broadcast-and-jamming phase, while the second phase is called the relaying phase, and the final phase is called CJ’s secondary phase, which is used for transmitting the secondary user message. More explicitly, CJs transmit noise for impairing the untrusted relay node’s ability to decode the message during the broadcast-and-jamming phase. In compensation for their help, CJs are allocated part of the available spectrum by the PU for their transmission during the secondary transmission phase. A Stackelberg leader–follower game was considered between the PU and the CJs, while a power control game that is based on the well-known Nash equilibrium is employed by the CJs. Furthermore, an investigation into the effect of invoking simultaneous transmission and time-division-based transmission scenarios during the CJs’ secondary transmission phase was carried out. Finally, we evaluated the achievable secrecy rate of the PU and the utility rate of the CJs in our proposed scheme.

Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

Mathematical model development for multivariate decision-making problems (i.e., multiple parameter and response optimization problems) has received significant attention and has been investigated by many researchers and practitioners. Although many different optimization models and methods, including priority and weight allocation problems, have been proposed in the literature, there is significant room for improvement. The majority of existing optimization methods may have difficulties in determining reliable priorities and weights for practical industrial situations. In addition, because they often focus on tradeoffs only among multiple output responses, these methods may not incorporate the multiple priority and/or weight effects directly from input factors to output responses (i.e., quality characteristics). To address these problems, the primary objective of this research is to propose a new multi-objective optimization approach by integrating a game theory principle (i.e., the Stackelberg leadership game) into a robust parameter design model to determine the optimal factor settings. First, a multi-response robust design optimization (RDO) problem was formulated using a mean squared error model and response surface methodology. A Stackelberg leadership game is then integrated into this RDO problem, where multiple responses play the role of game participants. Second, the integrated RDO model using the Stackelberg game-based multi-response (SGMR) formulation approach is analyzed by decomposition into various sequential optimization models in terms of different leader–follower relationships. Finally, non-dominated solutions are obtained from the proposed model by evaluating the overall quality loss (OQL). A pharmaceutical numerical example was performed to demonstrate the proposed integrated model and to examine whether this model can determine the most efficient solutions when the relative importance among multiple responses is unidentified. In addition, a comparative study associated with the conventional multi-objective optimization methods and the newly proposed RDO model is presented, and the proposed RDO model provided significantly better solutions than the conventional methods in the relevant comparative study.

How to finance the supply chain when you are small? Clearance sale and loan payment timing in financially constrained supply chains

Before inventory can be put into shelves at a retailer, it needs to be produced, which takes time. During this time traditionally the supplier had to cover the money bound in inventory, but new paradigms, such as supply chain finance, change who pays for work-in-process inventory. While this opens new possibilities for smaller, financially constrained suppliers, it puts additional financial pressure on the retailers. So, it may exclude smaller retailers, which are also cash constrained. If demand fluctuates then they may even have to recur to clearance sales to repay the loan. This study provides guidance to these small retailers on which clearance sale strategy to adopt, and when to repay their loans, investigating the interaction between both decisions using Stackelberg game framework in a dyadic supply chain where the supplier is the Stackelberg leader. It considers multiple bank interest rates and contract types chosen by the supplier. Results show that the retailer’s optimal order quantity decreases by adopting a limited clearance sale model for leftover disposal if it pays its loan immediately after the normal selling season. If it decides on loan payment after clearance sale, its optimal order quantity is not influenced by the clearance sale strategy, and we further demonstrate that the retailer’s optimal order quantity, loan payment timing, and expected profit are influenced by the supplier’s chosen contract. We find that buyback (BB) and revenue sharing (RS) contracts coordinate the supply chain only if the retailer resorts to a bank loan for inventory procurement.

Public private partnerships contract under moral hazard and ambiguous information

This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, with the possibility for the public to stop the contract. The public (“she”) pays a continuous rent to the consortium (“he”), while the latter gives a response characterized by his effort. Usually, the public cannot observe the effort done by the consortium, in addition, the law of the Agent’s effort which affects the distribution of the total output is to be chosen over a set of probabilities, leading to a Principal-Agent problem with moral hazard and Knightian uncertainty characterized by [Formula: see text]-ignorance. Our problem is formulated as a Stackelberg leadership model between the public and the consortium. This problem is solved in three steps. The first one consists on characterizing the worst case, then we derive the Agent’s best response. In the third step, we solve the Principal problem by maximizing the social value of the project minus the rent paid, which is a standard stochastic control problem. The public value function is characterized by the solution of an associated Hamilton–Jacobi–Bellman variational inequality. The public value function, the optimal effort and the optimal rent are computed numerically in a feedback form by using the Howard algorithm. We show numerically that each increase in the degree of Knightian uncertainty leads to increase the optimal effort, and decrease the value function.

Price leadership, spying, and secret price changes: a Stackelberg game with imperfect commitment

AbstractWe analyze price leadership in a Stackelberg game with incomplete information and imperfect commitment. Sequential play is induced by an information system, represented by a spy, that reports the price of one firm to its rival before the latter chooses its own price. However, the Stackelberg leader may secretly revise its price with some probability. Therefore, the spy’s message is only an imperfect signal. This gives rise to a complex signaling problem where both sender and receiver of messages have private information and the sender has a chance to take another action with some probability. We find partially separating and pooling equilibria that satisfy equilibrium refinements such as the intuitive criterion and support collusive outcomes.