Two-period Game Research Articles

Pricing and collection decisions of a closed-loop supply chain with remanufacturing under reciprocal preferences

This paper examines the effects of reciprocal preferences on the performances of a closed-loop supply chains (CLSC) with remanufacturing. Specifically, we incorporate reciprocal preferences into a two-echelon CLSC in which the manufacturer collects used products and then remanufactures the other parts except for key components as well as producing new products, and must purchase such key components from the supplier. Using a supplier-led Stackelberg game framework, the models are constructed with and without reciprocity, and then the effects of reciprocity on channel efficiency, consumers, environment and society are examined. We show that, (i) if the supplier reciprocates, the collection rate, the CLSC’s total profit, the channel efficiency and the consumer surplus enhance. Additionally, if only the manufacturer reciprocates, the CLSC’s profit remains constant; (ii) under certain conditions, the reciprocal preferences of both channel members aggravate environmental impact, while benefit social welfare; (iii) Pareto improvement can be achieved if the reciprocity parameters of both channel members are relatively high, and a simple procurement price contract can conditionally coordinate the CLSC. Finally, two extensions are studied by considering consumer heterogeneity and solving a two-period game problem, and the results characterize how reciprocal behaviors drive the performances of channel members.

The interaction of CM’s encroachment time and OEM’s outsourcing strategy when considering the cost-learning effect

Contract manufacturing has been widely studied in recent years. At the same time, existing research rarely considers when should the contract manufacturer (CM, she) launch a product of her own brand to encroach into the market. To fill this research gap, this study considers a two-period game consisting of one original equipment manufacturer (OEM, he) and one CM. The CM with a cost-learning ability could strategically decide whether and when to produce a final product of her own to encroach the market. The results show that when the OEM has a strong brand advantage, the CM may lose profit from encroachment into the market because her cost-learning capability contributes to grabbing the OEM’s market share and then the decrease in OEM’s orders hurts the CM herself in turn. On the contrary, facing a weak-brand-advantage OEM, the CM will encroach in both periods. Furthermore, the OEM can also derive advantages from the CM’s encroachment when the OEM possesses a strong brand advantage. However, when the OEM’s brand advantage is at a moderate level, refraining from encroachment will result in Pareto Optimality for both the OEM and CM.

Dynamic joint strategy of channel encroachment and logistics choice considering trade-in service and strategic consumers

As Internet technology develops rapidly, consumers’ consumption habits gradually shift from offline to online, and they are growing more strategic. In order to cater to strategic consumers, offline durable goods firms providing trade-in service are faced with practical issues of making dynamic strategies about whether establishing online channels and adopting which logistics service between self-logistics and third-party logistics (TPL) to deliver online orders. To tackle these problems, this study considers three scenarios and analyzes dynamic joint strategy of channel encroachment and logistics choice for a durable goods firm who owns an offline channel and offers trade-in service to strategic consumers via constructing a two-period game model. Results show that the firm’s dynamic joint strategy of channel encroachment and logistics choice will be affected by fixed operating cost, logistics service level difference and self-logistics cost. Moreover, trade-in service will have huge impacts on channel encroachment and logistics choice strategy. At last, when considering cap-and-trade policy, the service level of self-logistics and the cost of shipping used products, the optimal dynamic joint strategy of channel encroachment and logistics choice remains viable.

Conflict Under Incapacitation and Revenge: A Game-Theoretic Exploration

Abstract In real life, winning a conflict sometimes does not end the conflict. Revenge motivations can stay and provide momentum to the conflict, thus leading to further escalation of the conflict. This is known as the value effect or vengeance effect of revenge. However, the presence of revenge can lead to de-escalation of the conflict out of self-deterrence and sometimes retaliation out of revenge is not possible if the combatant is incapacitated. Hence, the impact of revenge on the level of violence is a priori not clear. This paper is an attempt to answer that question. Using a two-period game of conflict this paper tries to show how desire and capabilities of the combatants to exact revenge can influence the intensity of the conflict. This paper shows the following: how the strategies of the combatants are influenced by the value effect of revenge, self-deterrence and incapacitation of the combatants; how the stronger combatant is in a favourable position in the conflict and can prevent its opponent from going into second period conflict out of revenge; when the combatants are equally strong the intensity of the conflict starts falling with time. It also lays out some real-life conflicts and existing empirical work to support the results.

Debt crises between a country and an international lender as a two-period game

A two-period game between a country and an international lender is developed. In each period the country can repay debt, borrow from international credit markets, loan from an international lender, or default. The international lender can approve or deny the loan. The risk averse country maximizes a time-discounted utility incorporating its consumption. The international lender maximizes a time-discounted utility which values the country's consumption growth positively, and the debt-to-endowment ratio, the loan-to-endowment ratio, and the default penalty negatively. The subgame perfect equilibria are determined with backward induction. It is shown analytically that a country borrows less from international credit markets if it obtains a loan from an international lender and, intuitively, if its endowment increases. In contrast, the country borrows more if its future endowment (in period 2) can be expected to increase, or its initial borrowing is high. The model is simulated applying empirical data from the 2010 Greek crisis. The simulations illustrate how the country consumes in the two periods depending on whether the international lender approves or denies a loan. The impact is assessed of time discounting, risk aversion, default penalties, the country's endowment, interest rates, how the international lender values various characteristics of the country, and initial borrowing and consumption before the game starts.

Dynamic pricing and service customization strategy for IoT-based smart products

Digital technology has changed consumer behavior and expectations motivating firms to innovate customization strategies to meet the increasingly personalized needs of consumers. To explain this change, we first constructed a two-period game between a smart product manufacturer and a service customization platform. Second, we obtained optimal service customization strategies based on the impact of Internet of Things (IoT) technology. Finally, we implemented a case study of the smart product manufacturer ORVIBO and the Oppein MALL platform for whole-house customization to verify these optimal strategies. The results indicate that (i) firms should view the IoT's value in the long term, as their profits do not always increase as the IoT functionality level improves; (ii) the manufacturer's optimal strategy is to adopt service customization in both periods; (iii) service customization strategies can achieve Pareto optimality for the manufacturer and platform, resulting in a win-win state for consumers.

Voluntary green technology adoption: The effects of regulatory uncertainty and competition

Stricter environmental regulations force firms to adopt green technology. However, firms have realized that the more they voluntarily adopt green technology, the higher the probability that stricter new regulations will be enforced. Thus, firms may delay adopting green technology to resist stricter regulations. Conversely, some firms choose voluntary adoption to gain a market advantage over their rivals. Considering the impact of firms’ adoption decisions on the enforcement of new regulations and product competition, this study develops a two-period game model to investigate how competing firms adopt green technology when facing a potentially stricter regulation. The Nash equilibrium shows that if the basic probability of the new regulation is moderate, firms will differentiate their products through green technology to alleviate price competition; if the probability is high, firms will voluntarily adopt green technology; otherwise, they will wait until the government enforces a stricter regulation and mandates them to adopt green technology. Interestingly, our results show that potentially stricter regulations will induce firms to behave strategically. When firms’ green cost difference is small, competing firms will collude to delay stricter regulations by not adopting green technology. However, when firms’ green cost difference is significant, the low-cost firm tends to adopt green technology to lobby for new regulations and gain a cost advantage. Our work not only provides an economic explanation for the different adoption behaviors of firms but also provides managerial insights for competing firms as well as policy insights for the government.

Is AI testing beneficial for the manufacturer and social welfare? Optimal test strategy of a smart product

The rapid technological revolution of Industry 4.0 has set off rapid advancement in the smart product development. Testing the smart product’s system before release to market is crucial for ensuring proper functioning. Smart product manufacturers must carefully consider different testing modes to choose the optimal one based on product characteristics and consumer’s shopping intention. Additionally, different testing modes have varying impacts on the environment and social welfare, as well as profitability of the product. This study utilizes a two-period game theory model to analyze a smart product manufacturer’s optimal testing mode and pricing decision. Three testing mode are evaluated: manual testing mode (MT mode), artificial intelligence testing mode (AT mode), and public testing mode (PT mode). Consumers’ utility is influenced by factors such as consumer preferences, product quality, usage duration, and network externality effect. Our findings indicate that the optimal testing mode depends on quality improvement and network effect coefficients. Specifically, when the degree of quality improvement is high and the network effect is moderate, MT mode is preferred; when the quality improvement is high but the network effect is small, AT mode dominates; under other conditions, PT mode is optimal. Quality improvement and network effect coefficients have similar effects on pricing decisions but impact the profits in different manners. Social welfare is the highest under MT mode when the network effect is high and quality improvement is low, under AT mode when network effect is low and quality improvement is high, and under PT mode when both factors are high or low. Finally we provide a numerical example of how profit-driven business decisions may conflict with social welfare, potentially leading to lower social welfare than the theoretical optimum under the chosen testing mode strategy.

Optimal government subsidy scheme for lean-oriented innovation in the textile industry

The increasing environmental burden posed by the textile industry has placed pressure on firms to shift to sustainability through lean-oriented innovation (LOI). However, firms' LOI incentives may be weakened by high investment costs. Recognizing firms' predicaments, governments are developing subsidy policies to promote LOI. This study builds a two-period game model to explore optimal government's subsidy decisions for LOI in an evolving textile industry, incorporating government subsidies, LOI investment, and firms' production decisions. The study reveals that the social welfare in period two exceed those in period one, implying that competition in the industry improves social welfare. Furthermore, we derive government subsidy decisions for maximal environmental protection and social welfare and find that the former does not necessarily lead to a superior environmental performance to the latter. Moreover, we find that under some conditions, a “win-win-win” situation can be reached when the government pursues social welfare optimum.

Carbon allowance approach for capital-constrained supply chain under carbon emission allowance repurchase strategy

PurposeThe purpose of this study is to investigate which of the two carbon allowance allocation methods (CAAMs), i.e. grandfathered system carbon allowance allocation (GCAA) and baseline system carbon allowance allocation (BCAA), is more beneficial to capital-constrained supply chains under the carbon emission allowance repurchase strategy (CEARS).Design/methodology/approachAdopting CEARS to ease the capital-constrained supply chains, this study develops two-period game models with manufacturers as leaders and retailers as followers from the perspective of profit and social welfare maximization under two CAAMs (GCAA and BCAA), where the first period produces normal products, and the second period produces low-carbon products.FindingsFirst, higher carbon-saving can better use CEARS and achieve a higher supply chain profit under the two CAAMs. However, the higher the end-of-period carbon price is, the lower the social welfare is. Second, when carbon-saving is small, GCAA achieves both economic and environmental benefits; BCAA reduces carbon emissions at the expense of economic benefit. Third, the supply chain members gain higher profits and social welfare under GCAA, so the government and supply chain members are more inclined to choose GCAA.Originality/valueBy analyzing the profits and total carbon emissions of capital-constrained supply chains under GCAA and BCAA, this study provides theoretical references for retailers and capital-constrained manufacturers. In addition, by comparing the difference in social welfare under GCAA and BCAA, it provides a basis for the government to choose a reasonable CAAM.

Deterring Sellers’ Cheap Talk Actions via Online Rating Schemes

This paper develops a two-period game theoretic model to investigate a seller’s quality claims in a cheap-talk setting. In this model, consumers are reference-dependent with respect to product quality, and consumers who have purchased items can share their quality assessments via online ratings; additionally, consumers may be naive or experienced: naive consumers simply believe the quality claims and quality assessments, whereas experienced consumers can accordingly make rational quality inferences. We find that, in the scenario with only naive consumers, when the reference effect is weak, the seller will always claim the highest quality; when the reference effect is strong, the low-quality seller will claim the highest quality, whereas the high-quality seller will understate its products’ quality. In the scenario with only experienced consumers, the seller will claim some moderate quality levels. In the scenario with both types of consumers, in period one, the low-quality seller will always claim some moderate quality levels to serve both types of consumers, whereas the high-quality seller will claim the highest quality when the reference effect is extremely weak and thus serve only naive consumers, or it will adopt truth-telling otherwise; in period two, the low-quality seller will charge a higher price to serve only experienced consumers, whereas the high-quality seller will charge a lower price to serve both types of consumers.

Optimal pricing strategy in a dual-channel supply chain: A two-period game analysis

<p style='text-indent:20px;'>With the development of e-commerce and the rapid updating of products, multi-period pricing has been widely attempted in dual-channel supply chains. In this paper, we develop a two-period game-theoretical model to investigate the problem of two-period pricing and strategy choice for a dual-channel supply chain in which a manufacturer sells a product through its direct channel and an independent retailer. The two common pricing strategies, i.e., dynamic pricing and preannounced pricing, are considered. Through analyzing and comparing, we derive a unique Stackelberg equilibrium under the two pricing strategies and find that dynamic pricing dominates preannounced pricing and achieves a win-win result for the retailer and the manufacturer. Moreover, under this strategy, the manufacturer charges a higher or lower direct price in the second period than in the first period depending on channel competition, whereas the retailer always set a lower retail price in the second period. Finally, we extend our models to consider a unique wholesale pricing strategy, the profit discount factor, and different decision sequences for the selling prices of the two channels. We show that our main results are robust, except that the decision sequence changes the optimal pricing strategy choice of the retailer.</p>

Dynamic pricing of a manufacturer producing new/remanufactured products with consideration of strategic green consumers

<p style='text-indent:20px;'>Flourishing sales of new and remanufactured products have promp-ted firms to design different pricing strategies for strategic green consumer behavior. To this end, this paper studies a pricing strategy by developing a two-period game model in a remanufacturing system by considering the period and product discounts. Here, the manufacturer has two pricing strategies: <i>dynamic pricing</i> and <i>compensation pricing</i>. Unlike the extant literature on strategic consumers, this paper considers heterogeneous products existing in a remanufacturing system and focuses on how strategic/green consumption behavior affects the pricing strategy. The results through numerical studies indicate that when the consumers' preference for remanufactured products is high, or consumers are short-sighted, the manufacturers prefer a dynamic pricing strategy; in all other cases, a compensation pricing strategy is preferred. Conversely, a manufacturer looking to the long-term benefits favors a compensation pricing scenario. Overall, the green segment is beneficial to the manufacturer, especially when primary consumers show a high preference for remanufactured products.</p>

Co-Opetition Strategy for Remanufacturing the Closed-Loop Supply Chain Considering the Design for Remanufacturing

The co-opetition strategy between manufacturers and remanufacturers is a key problem of the closed-loop supply chain, especially for the manufacturers often facing decision-making dilemmas when undertaking the environmental responsibilities of the design for remanufacturing (DfRem). Since DfRem is thought to be advantageous for recycling and remanufacturing, it will lower the production costs for remanufacturers but raise them for manufacturers. On the other hand, manufacturers cannot abandon the DfRem because of environmental responsibilities. This work thus formulates three two-period game models of the competition model with patent protection, the competition model without patent protection, and the cooperation model, which consists of a manufacturer and a remanufacturer, to investigate the decision of the manufacturer and remanufacturer co-opetition strategies. The price, the level of DfRem, the recovery rate, the profit, and other factors are compared across the three models using reverse induction and numerical simulation. In addition, we analyzed the influence of different equilibrium solutions on customer willingness to pay for remanufactured products. We find that cooperation not only contributes to the improvement of DfRem but is also the best choice to ensure the stable development of the supply chain system. Manufacturers, in particular, prefer to work together wherever feasible and actively pursue collaboration rather than advocating for patent protection to fend against remanufacturers, even when they have patent rights.

Markdown pricing strategy under a dual-channel supply chain with strategic consumers

This study investigates the markdown pricing strategies for a manufacturer and a retailer in a two-period dual-channel supply chain, where the manufacturer sells its products via its own direct channel and an independent retail channel to strategic consumers who may wait for markdowns. A two-period game is developed to systematically study the optimal regular prices and markdown prices under four cases, i.e., no markdown in both channels, markdown only in the direct channel, markdown only in the retail channel, and markdowns in both channels. By comparing the different cases, we find that the manufacturer benefits most from the case with markdowns in both channels, where the markdown rate of the retail channel is lower than that of the direct channel. On the other hand, the results indicate that the retailer may also profit most from the case with markdowns in both channels when the consumer acceptance of the direct channel is sufficiently high; otherwise, the retailer enjoys the highest profit under the case with markdown only in the retail channel. Finally, it is found that strategic consumer behavior has a positive impact on the retailer’s profit but a negative impact on the manufacturer’s profit.

Launch strategies for luxury fashion products in dual-channel distributions: Impacts of social influences

Many studies show that social influences from purchase activities of fashion leaders and followers significantly affect luxury fashion management. Some luxury fashion manufacturers employ both direct and retail channels to sell products. Mostly, they launch new styles through direct channels initially. Thus, to ascertain whether this is the best strategy, this study constructs a two-period game model to examine the effects of social influences on channel sequence and pricing decisions in a dual-channel distribution system. The manufacturer can choose one of two alternative strategies: launching the product through direct channel first and through retail channel first. Our findings show that social influences significantly affect channel sequence and pricing decisions. If the impacts of social influences are high, the most profitable strategy for the manufacturer is to launch the new product through the retail channel first. In contrast, under this condition, the most profitable strategy for the retailer is to sell the product later than the direct channel. If the market size of fashion followers is larger than that of fashion leaders, social influences have a positive effect on both direct and retail prices under any strategy. This study primarily investigates the impacts of social influences on channel sequence and pricing decisions in a dual-channel distribution system for luxury fashion products.

Prevention and adaptation to diversified risks in the seaport–dry port system under asymmetric risk behaviors: Invest earlier or wait?

The special geographical locations and socioeconomic functions of seaports and dry ports in the global trading system render them vulnerable to diversified risks. Targeted preventive and adaptive investments can reduce the probability and potential damage of corresponding risks. This study proposes a two-period game to explore the scale and timing of prevention and adaptation by seaport and dry port authorities regarding regular and disruption risks in a competitive environment under ambiguity and asymmetric risk behaviors. The results show that risk aversion increases prevention and adaptation while risk probability ambiguity aversion decreases prevention and adaptation under the effect of information accumulation. Under risk aversion, early prevention and late adaptation are best for port authorities, whereas waiting until the next period to invest is a better option in regard to ambiguity aversion as long as the ambiguity of risk probability can be reduced through information accumulation. Moreover, we extend the risk sensitivity and probability ambiguity models to seaports and dry ports that cooperate and exhibit a leader-follower relationship. Our analysis shows that the cooperative relationship leads to the free-rider effect among port authorities, while the leader-follower relationship enables the seaport and dry port authorities to achieve a Nash equilibrium when choosing early prevention or late adaptation. The findings offer significant economic and managerial insights for the decision-making and policy-making of ports and government authorities.

The optimal green strategies for competitive ocean carriers under potential regulation

Uncertain green regulation and market competition are two major external environmental factors for ocean carriers to consider when making their decisions on business operations. The uncertainty of the green regulation arises from the probability of its occurrence. It is assumed that ocean carriers can adopt one of the two green strategies, i.e., the equipment upgrade strategy or the slow steaming strategy, to comply with the potential green regulation. This paper aims to examine the stable green strategies as well as the pricing decisions of competitive carriers in the shipping market considering the service differentiation and the upgrade risk. A two-period game model is formulated to seek the sub-game perfect Nash equilibrium under potential regulation. We obtain the final sub-game perfect Nash equilibrium, i.e., when the probability of enacting regulation is sufficiently high, there is always one carrier that will adopt the equipment upgrade strategy. However, because of the joint impact of market competition and uncertain regulation, the two carriers will never adopt the equipment upgrade strategy simultaneously. In addition, our results show that the potential regulation sometimes may help the two carriers achieve the optimal outcome. Nevertheless, the carriers may fall into a “sub-optimal outcome” in some situations.

Strategic decision in a two-period game using a multi-leader-follower approach. Part 2 – Decision making for the new player

Strategic decision in a two-period game using a multi-leader-follower approach. Part 2 – Decision making for the new player

Strategic decision in a two-period game using a multi-leader-follower approach. Part 1 – General setting and weighted Nash equilibrium

Strategic decision in a two-period game using a multi-leader-follower approach. Part 1 – General setting and weighted Nash equilibrium