Stackelberg Leader Research Articles

Applications of Blockchain Technology in Sustainable Fashion Supply Chains: Operational Transparency and Environmental Efforts

Using environmentally friendly materials is a popular business practice in the fashion industry nowadays, which can affect both a fashion product's cost and its environmental impacts in the manufacturing process. Given the growing social consciousness of the public, the integration of environmentally friendly materials can also influence the market demand of fashion products. This article studies the information disclosure games over the environmental efforts in fashion supply chains. We consider a fashion retailer, which is the Stackelberg leader, orders sustainable fashion products made from environmentally friendly materials from a manufacturer. The fashion retailer can choose either to affix the eco-label or to adopt the blockchain technology, to declare the environmental quality of the fashion product to consumers. Meanwhile, given that the environmental quality is unobservable to the fashion retailer and the consumers, the manufacturer with credibility concerns can have the actual environmental quality of the fashion product discounted. We discuss how the application of the blockchain technology influences the information disclosure games over the environmental efforts in the fashion industry. Findings in this article advance the understanding on the application of the blockchain technology in sustainable practices in fashion supply chains.

Fresh Agricultural Products Supply Chain Coordination and Volume Loss Reduction Based on Strategic Consumer.

The reduction of fresh agricultural product volume loss throughout the supply chain system is of high importance due to their perishable nature and impact on society, the economy, and environment. In this paper, three models for two-stage pricing, coordination, and volume loss reduction of the supply chain where third-party logistics service providers and retailers act as a Stackelberg leader and a follower for fresh agricultural products are developed, taking into account both volume loss during transport and quality loss in retail in the presence of strategic consumers. The following results are drawn from the contract for sharing revenues and service costs: (1) The supply chain achieve coordination and the products are healthier for consumers; (2) the coordination leads to a reduction in the three types of volume losses simultaneously only if the lowest marginal costs of the supply chain occur under certain conditions; and (3) the increase in the service sensitivity coefficient, the increase in the freshness discount coefficient under certain conditions, the decrease in the consumer benefit discount coefficient under certain conditions, and the decrease in the price sensitivity coefficient lead to an increase in the profit of the supply chain and a reduction in the three types of volume losses.

Overconfidence and Timing of Entry

We analyze the impact of overconfidence on the timing of entry in markets, profits, and welfare using an extension of the quantity commitment game. Players have private information about costs, one player is overconfident, and the other one rational. We find that for slight levels of overconfidence and intermediate cost asymmetries, there is a unique cost-dependent equilibrium where the overconfident player has a higher ex-ante probability of being the Stackelberg leader. Overconfidence lowers the profit of the rational player but can increase that of the overconfident player. Consumer rents increase with overconfidence while producer rents decrease which leads to an ambiguous welfare effect.

Rawlsian fairness in push and pull supply chains

We study a dyadic supply chain with firms following the Rawlsian principle of fairness and examine its impact on chain performance and firms’ profits. Different from the inequality-aversion model in the distributional fairness literature, the participants with the Rawlsian fairness concern maximize the profit of the disadvantageous party according to their own fairness criteria. Our results show that the Rawlsian principle adopted by individual firms can achieve not only fairness but also Pareto efficiency. By studying both push and pull supply chains, we find that what matters is the decision sequence between the manufacturer and the retailer. The fair-minded Stackelberg follower can induce the Stackelberg leader, no matter fair-minded or not, to offer a coordinating wholesale price. The chain coordination can be achieved only if the follower is not too demanding (i.e., it does not demand an excessively high portion of chain profit according to its fairness criterion). Additionally, a win-win outcome can be achieved, provided the follower is not too humble. All else being equal, the win-win region is larger with a higher demand uncertainty. Last but not least, we compare our results with those under the inequality-averse fairness model on a push supply chain and find that the parameter ranges of coordination and win-win are wider when the participants follow the Rawlsian principle of fairness.

Common Retailer Channel Revisited: The Role of Supply Network Size

This study is motivated by the ubiquitous practical existence of common retailer distribution channels (e.g., a grocery store offering multiple brands of the same product). Demand interdependence (product substitutability) among various brands is critical and thus we investigate its impact on firms’ profits. Using an economic framework with manufacturers operating as Stackelberg leaders, our analysis reveals unique and substantive insights dependent on the underlying market demand structure, and in some cases, the extent of supply coverage. For the Spence–Dixit–Vives demand structure, we find that competing manufacturers prefer to offer brands with low levels of substitutability while retailer’s preferences are moderated by the interaction effect between the number of competing brands and level of product substitutability (essentially the retailer prefers high levels of substitutability when the number of brands is “small," and vice versa). For the Shubik–Levitan demand structure, manufacturers may prefer high or low levels of product substitutability depending on the extent of supply coverage while the retailer always prefers high levels of product substitutability. These findings offer useful prescriptions for category management and persuasive advertising.

Approximate Calculation of Equilibria in the Nonlinear Stackelberg Oligopoly Model: A Linearization Based Approach

The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. Necessary conditions for the existence of a solution of a system of nonlinear equations with power functions are established. The system of equations for the optimal responses of agents is linearized by expanding the power functions in Taylor series. As a result, the linearized system depends on the vector of linearization parameters, and the calculation of game equilibria is reduced finding fixed points of nonlinear mappings. The deviations of the approximate equilibrium from the exact solution are investigated. Analytical formulas for calculating equilibria in the game of oligopolists under an arbitrary level of Stackelberg leadership are derived. Analysis of duopoly and tripoly demonstrates that the game equilibrium is determined by two factors as follows. First, the concavity of the agent’s cost function (the positive scale effect) leads to an increase in his payoff compared to the agents with convex cost functions (the negative scale effect). Second, the agent’s payoff increases if he is a Stackelberg leader; however, the advantage of his environment by the type of cost function reduces the effect of the second factor.

Pricing strategies for O2O business model considering service spillover and power structures

AbstractIn contradistinction to the traditional dual‐channel retail model, the online and offline channels are two business units of a single retailer in an online to offline (O2O) business model. The service‐related effort of the offline channel has a spillover effect on the online channel. This paper establishes three game‐theoretic models to analyze how service spillover and power structures affect supply chain members’ performance in the O2O business model. The main results are as follows. First, a service spillover effect is always beneficial to the manufacturer's profit due to the increasing wholesale price and total demand in all three scenarios. Second, unlike the traditional dual‐channel model, service spillover does not inevitably cause price competition in the O2O dual‐channel model. Under different power structure conditions, the spillover intensity has a significant effect on the retailer's profit and service strategy. When the manufacturer is a Stackelberg leader, the effects of spillover on a retailer's profit depend on online channel acceptance level and service level. A service differentiation strategy can help the retailer increase profit margins under certain situations. When the manufacturer and retailer have the same power, retailer's profit increases with spillover intensity, and a service consistency strategy can be implemented. When the retailer is a Stackelberg leader, the retailer's profit decreases first and then increases, and a service mixed strategy will reduce the loss of retailer's profit. Finally, the switch in dominant power between manufacturer and retailer has no impact on retail prices and demand. The total supply chain profit in two Stackelberg models is also equivalent, but lower than that in the Nash model.

Incentive mechanisms in a green supply chain under demand uncertainty

This paper studies a couple of incentive mechanisms for collaborative enhancing the green degree of products in a retailer-driven supply chain consisting of one risk-averse downstream retailer and one risk-averse upstream supplier under demand uncertainty. The retailer, acting as the Stackelberg leader, decides the retail price of green products. While the supplier, acting as the follower, is answerable for the green degree of products. We provide three contracts in order to enhance the green degree of products: wholesale price contract, reward contract without target green degree, and reward contract with target green degree. Then, we make out the influence of the retailer’s incentive on the supplier’s green efforts through the above contracts and the impact of the members’ risk aversion preference on the supply chain performance. The analytical results imply that the proposed incentive mechanisms can contribute to the product greenness and the overall utility improvement of the supply chain. Furthermore, under the reward contract with target green degree, the supplier is promoted to produce the greenest products and the overall utility of the supply chain can be the largest among the above three contracts. The results also suggest that the risk aversion attitudes of supply chain members have an adverse effect on the utilities of themselves and the whole supply chain. Finally, based on theoretical analysis and numerical studies, we provide both managerial and practical suggestions for green supply chain management.

Optimal Siting, Sizing, and Enforcement of Marine Protected Areas

The design of protected areas, whether marine or terrestrial, rarely considers how people respond to the imposition of no-take sites with complete or incomplete enforcement. Consequently, these protected areas may fail to achieve their intended goal. We present and solve a spatial bio-economic model in which a manager chooses the optimal location, size, and enforcement level of a marine protected area (MPA). This manager acts as a Stackelberg leader, and her choices consider villagers’ best response to the MPA in a spatial Nash equilibrium of fishing site and effort decisions. Relevant to lower income country settings but general to other settings, we incorporate limited enforcement budgets, distance costs of traveling to fishing sites, and labor allocation to onshore wage opportunities. The optimal MPA varies markedly across alternative manager goals and budget sizes, but always induce changes in villagers’ decisions as a function of distance, dispersal, and wage. We consider MPA managers with ecological conservation goals and with economic goals, and identify the shortcomings of several common manager decision rules, including those focused on: (1) fishery outcomes rather than broader economic goals, (2) fish stocks at MPA sites rather than across the full marinescape, (3) absolute levels rather than additional values, and (4) costless enforcement. Our results demonstrate that such naïve or overly narrow decision rules can lead to inefficient MPA designs that miss economic and conservation opportunities.

Reflexion Processes and Equilibrium in an Oligopoly Model with a Leader

An oligopoly model with a leader in the class of linear demand and cost functions of agents is considered, and the dynamic processes of reflexive behavior in this model are analytically studied. Dynamic decision-making processes with the inaccurate beliefs of agents about the choice of competitors are implemented not through the optimal responses to their expected actions, but as repeated static games on a range of admissible responses. Such an approach to decision-making is demonstrated to be justified. Observing the current state of the market and considering current economic restrictions (competitiveness and profit), agents refine their outputs in game-to-game dynamics and take steps towards the current position of their goal. A Stackelberg leader and other agents with the Cournot response choose step sizes independently of each other. Sufficient conditions on the step sizes under which the dynamics converge to an equilibrium are established.

Will the community O2O service supply channel benefit the elderly healthcare service supply chain?

This paper studies the coordination of the elderly healthcare service supply chain (EHSSC) within a dual-channel setting. A game-theoretic framework is introduced to analyse how best the elderly service integrator (ESI) and elderly service provider (ESP) would make decisions and interact amidst cooperation and competition. Three cases including the centralised case, the Bertrand game case and the Stackelberg game case are examined to obtain the optimal relationship structure suitable for the EHSSC coordination. The associated loss due to customer dissatisfaction and the value increment due to the ESI’s service enhancement effort are incorporated in the model. Also, by considering customer’s health status, optimal pricing strategies are investigated for both the ESI and ESP under two different service demand classes. The main results are summarised as follows. First, the value increment due to the ESI’s service enhancement effort may have different impacts on the ESP’s prices in different service demand classes. Second, the whole supply chain would achieve effective coordination when the ESP acts as the Stackelberg leader with an appropriate setting of the wholesale price. Third, a lower wholesale price set by the ESP could benefit both the ESI and ESP in achieving greater demand and profit.

Strategic analysis of RFID adoption sequences in a supply chain with Cournot competition: effects of ordering-timing strategies

We investigate the effects of ordering-timing strategies on radio-frequency identification (RFID) adoption sequences and firms’ profitability in a supply chain with a manufacturer and two retailers, both of whom suffer from misplaced inventory problems. The manufacturer is the Stackelberg leader, the two retailers engage in a quantity competition and simultaneously/sequentially make decisions on RFID adoption under two ordering-timing strategies. We derive the equilibrium strategies for RFID adoption and characterize each partner’s optimal order quantity and profit. We show that the equilibrium strategies for RFID adoption are identical regardless of the two competing retailers’ RFID adoption sequences. The retailer with a smaller misplacement rate will never adopt RFID alone. However, for the retailer with a higher misplacement rate: the more intense the competition is, the more likely he is to adopt RFID; ordering later always promotes him to adopt RFID; ordering earlier is more attractive than adopting RFID when the tagging cost is intermediate. Furthermore, as long as one or both retailers adopt RFID, ordering simultaneously can achieve Pareto improvement for both retailers. When neither retailer adopts RFID, the optimal ordering strategies depend on the misplacement rates and competition intensity.

Six Types of Ambiguity in a Ramsey Climate Policy Model

While the scientific community is in general agreement about the nature and threat of global warming, the public and many political leaders are not. This paper casts the lack of full agreement as an instance of belief heterogeneity giving rise to six potential types of ambiguity with differing implications for carbon taxation and fiscal policy. Treating the Ramsey planner as a Stackelberg leader and private agents as followers, I distinguish three types of policy regime: (i) a political regime that strategically adopts the private sector's beliefs, (ii) a paternalistic regime that trust its own model only, and (iii) a pessimistic government with its own doubts about the climate model. The beliefs of private agents are represented by martingale multiplier perturbations M to a common approximating probability function and may be of two kinds: for pessimists}, M is a device to construct robust Euler conditions; for optimists, M is arbitrary and unknown to the planner, hence a source of ambiguity. The six proposed types of ambiguity differ in what the planner is ambiguous about, what private agents and the government know, and what the government believes private beliefs to be. In all instances, ambiguity induces robustness in policy and/or private decision rules affecting the social cost of carbon, and carbon and capital taxation. This paper shows further that, crucially, the carbon tax is not independent of other elements in fiscal policy. The results are framed in terms of distorted Arrow-Debreu pricing theory to show that the optimal carbon tax is equivalent to the permit price of an underlying asset---the government-imposed limit on emissions in economies with cap and trade.

Two-Echelon Supply Chain Model with Demand Dependent On Price, Promotional Effort and Service Level in Crisp and Fuzzy Environments

This article explores a supply chain model consisting of a single manufacturer and two competing retailers. The manufacturer, as a Stackelberg leader specifies a wholesale price and bears servicing costs of the products. Then, both the retailers advertise the products and sell them to the customers. So, the demand of the products is influenced by selling price, service level and also promotional effort. On the basis of this gaming structure, two mathematical models have been formed - crisp model, where each member of the chain exactly knows all the cost parameters and fuzzy model where those cost parameters are considered as fuzzy numbers. Optimal strategies for the manufacturer and the retailers are determined and some numerical examples have been given. Finally, how perturbations of parameters affect the profits of the chain members have been determined.

Warehouse Location in An Emerging Country: A Win–Win Proposition?

Warehouse solutions in emerging countries near suppliers have been adopted to achieve cost efficiency in offshore procurement. Previous academic literature ignores logistics operations costs in supply chain contracting. In this paper, we study contracting between a retailer in a developed country and a supplier in an emerging country while incorporating total landed cost (including logistics operations costs) in contracting. The retailer faces stochastic demand and stochastic lead time and determines the warehousing strategy. She can hold cycle stock and safety stock at the retail location (developed country warehousing) or allow the supplier to hold second‐tier cycle stock at a warehouse in the emerging country in addition to her holding inventory at the retail location (emerging country warehousing). We study the retailer’s optimal warehousing strategy in a centralized supply chain and a decentralized supply chain with the retailer as the Stackelberg leader. When emerging country warehousing is adopted in the decentralized supply chain, the retailer and supplier could achieve a win–win or a win–lose outcome compared to developed country warehousing. Our results show that the retailer’s warehousing strategies in the centralized and decentralized supply chains could be different. We further study the retailer’s optimal warehousing strategy under the Nash bargaining framework where the wholesale price and logistics decisions are negotiated simultaneously given the warehousing strategy. We compare this contract to that where logistics costs are excluded from contract negotiation. Our results show that by including logistics costs into contract negotiation the retailer and supplier could achieve lose–win, win–win and win–lose outcomes.

Aggregative games and oligopoly theory: short‐run and long‐run analysis

AbstractWe compile an IO toolkit for aggregative games with positive and normative comparative statics results for asymmetric oligopoly in the short and long run. We characterize the class of aggregative Bertrand and Cournot oligopoly games, and the subset for which the aggregate is a summary statistic for consumer welfare. We close the model with a monopolistically competitive fringe for long‐run analysis. Remarkably, we show strong neutrality properties in the long run across a wide range of market structures. The results elucidate aggregative games as a unifying principle in the literature on merger analysis, privatization, Stackelberg leadership, and cost shocks.

The Properties of Conjectural Variations in the Nonlinear Stackelberg Oligopoly Model

The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. The conjectural variations of each agent, i.e., the expected responses (changes in actions) of his counteragents that optimize their utility functions, are studied. Formulas for calculating the conjectural variations of each agent and also the sum of the conjectural variations of all agents in the environment of each agent are derived. The signs of conjectural variations under an arbitrary level of Stackelberg leadership are analyzed. The following properties of conjectural variations are established: 1) the variations are negative if the cost functions of all environmental agents are either convex or concave; 2) the variations are positive if the agents with concave cost functions (the ones with the positive scale effect) prevail in the environment over the agents with convex cost functions (the ones with the negative scale effect). The sum of the agent’s conjectural variations is: 1) negative and its magnitude is bounded above by 1 if the environmental agents mainly have convex cost functions; 2) positive and unlimited if the agents with concave cost functions prevail in the environment.

Emission reduction and market encroachment: Whether the manufacturer opens a direct channel or not?

This paper investigates the equilibrium strategies considering abatement decision and manufacturer encroachment in a supply chain, in which the manufacturer is a Stackelberg leader and the retailer is a follower. The manufacturer first determines the channel structure to distribute products through only the retail channel structure, only the direct channel structure, or the dual-channel structure. After that, the manufacturer and the retailer sequentially decide to sell a low-carbon product or a common product. The optimal prices, order quantities and profits under different combinations of channel structure and abatement decision are characterized. We observe that both firms prefer to invest in emission abatement under a sole channel structure if consumers have eco-friendly preference, while the equilibrium emission abatement strategies for the dual-channel structure depend on the investment cost coefficient and revenue-sharing coefficient. Under encroachment, the manufacturer is always better off while the retailer is worse off except for selling low-carbon product through the direct channel with a high consumer’s eco-friendly preference. In addition, when the consumer’s eco-friendly preference is moderate, selling low-carbon product may be a scourge for the retailer if the manufacturer has an encroachment ability. Further, the manufacturer should always post the direct channel’s order quantity after observing the retail channel’s order quantity under the dual-channel structure.

Information Sharing in a Supply Chain With a Coopetitive Contract Manufacturer

This paper studies information sharing in a supply chain where a contract manufacturer (CM) acts as both an upstream partner and a downstream competitor to an original equipment manufacturer (OEM). To better explore the effect of information sharing on a coopetitive supply chain, we consider a sequential game with the OEM as the Stackelberg leader under two different wholesale pricing methods, which is close to the practical situation. Our analysis shows that when the wholesale price is exogenously given, information sharing is beneficial for the OEM but hurts the CM, and a side-payment contract is designed to induce Pareto-optimal information sharing. When the wholesale price is a decision variable, the CM benefits from information sharing while the OEM does not and a discount-based wholesale price contract is designed to induce truthful information sharing. The numerical examples analysis further finds that the OEM benefits from the exogenous wholesale price scenario while the CM benefits from the endogenous wholesale price scenario. The study sheds lights on the decision-making processes for operating and managing the coopetitive supply chain and extends the research scope of information sharing. Our findings also provide some scientific references about information sharing in daily production.

Strategic Trade Policies under International Process R&D Competition with or without Market Leaders

Purpose - The purpose of this paper is to study strategic trade policies under international process research and development (R&D) competition with or without market leaders for free trade and a subsidy regime and compare the effects of R&D subsidies and export subsidies on the equilibrium levels of firm profit and social welfare. Design/methodology - For the analysis, we use previous work by Haaland and Kind (2008) and construct a differentiated goods duopoly model, wherein two firms compete via quantity in a thirdcountry market for free trade and the subsidy regime. We consider simultaneous-move quantity competition when the two firms choose their quantities simultaneously and sequential-move quantity competition when they choose their quantities sequentially. The results are compared to those of Balboa, Daughety and Reinganum (2004), who studied export subsidies. Findings - The following are the findings. First, the results of firm preference orderings regarding firm position from Dowrick (1986) and Balboa, Daughety and Reinganum (2004) may not hold in our model when the firms’ strategies are strategic substitutes under free trade. Second, the preference rankings under Cournot competition for free trade and a subsidy regime are the same as those in the strategic trade policy of export subsidy. Third, except for the cases of too close substitutes and complements, the results of firm and government preferences regarding firm position are different from those of Balboa, Daughety and Reinganum (2004) in that Stackelberg leadership in a subsidy regime is advantageous when the goods are substitutes but is disadvantageous when the goods are complements. Moreover, the equilibrium level of firm profit is the highest in the Cournot-Nash play when the goods are substitutes in a subsidy regime. Fourth, except for the cases of too close substitutes and complements, the results of firms’ and their respective governments’ trade regime preferences are similar to those of Balboa, Daughety and Reinganum (2004) in that a Stackelberg leader firm and government prefer free trade if the goods are substitutes and prefer a subsidy regime if the goods are complements. Furthermore, a Stackelberg follower firm and government strongly prefer a subsidy regime to free trade. Originality/value - By analyzing the effects of R&D subsidies and export subsidies in international markets, we can find similarities and differences between them in international markets.