Product-design and pricing strategies with remanufacturing

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

Controlled predatory pricing in a multiperiod Stackelberg game: an MPEC approach

We analyze a multiperiod oligopolistic market where each period is a Stackelberg game between a leader firm and multiple follower firms. The leader chooses his production level first, taking into account the reaction of the followers. Then, the follower firms decide their production levels after observing the leader’s decision. The difference between the proposed model and other models discussed in literature is that the leader firm has the power to force the follower firms out of business by preventing them from achieving a target sales level in a given time period. The leader firm has an incentive to lower the market prices possibly lower than the Stackelberg equilibrium in order to push the followers to sell less and eventually go out of business. Intentionally lowering the market prices to force competitors to fail is known as predatory pricing, and is illegal under antitrust laws since it negatively affects consumer welfare. In this work, we show that there exists a predatory pricing strategy where the market price is above the average cost and consumer welfare is preserved. We develop a mixed integer nonlinear problem (MINLP) that models the multiperiod Stackelberg game. The MINLP problem is transformed to a mixed integer linear problem (MILP) by using binary variables and piecewise linearization. A cutting plane algorithm is used to solve the resulting MILP. The results show that firms can engage in predatory pricing even if the average market price is forced to remain higher than the average cost. Furthermore, we show that in order to protect the consumers, antitrust laws can control predatory pricing by setting rules on consumer welfare.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Stochastic competitive entries and dynamic pricing

How should firms price new products when they do not know the timing, nor the nature of the next competitive entry? To guide managers’ pricing decisions in such contexts, we propose a dynamic pricing model with two types of randomly timed entry, i.e. imitative and innovative. The characterization of the equilibrium strategies reveals how optimal prices vary with the manager’s knowledge about the timing of future competitive entries. We show that price skimming is not always optimal when entry dates are unknown to managers. Everything else equal, we demonstrate that the randomness of competitive entries make forward looking managers to choose constant prices, even though the characteristics of the market would have justified skimming the demand in the normal course. Moreover, we show that the constant pricing policy remains optimal even when the incumbent’s optimal pricing strategy influences the probability of facing a competitive entry. Finally, we find that uncertainty does not necessarily hurt firms’ profits.     

Analyzing online B2B exchange markets: Asymmetric cost and incomplete information

This research applies the discriminating auction to analyze the online B2B exchange market in which a single buyer requests multiple items and several suppliers having equal capacity and asymmetric cost submit bids to compete for buyer demand. In the present model, we examine the impact of asymmetric cost and incomplete information on the participants in the market. Given the complete cost information, each supplier randomizes its price and the lower bound of the price range is determined by the highest marginal cost. In addition, the supplier with a lower marginal cost has a larger considered pricing space but ultimately has a smaller equilibrium one than others with higher marginal costs. When each supplier’s marginal cost is private information, the lowest possible price is determined by the number of suppliers and the buyer’s reservation price. Comparing these two market settings, we find whether IT is beneficial to buyers or suppliers depends on the scale of the bid process and the highest marginal cost. When the number of suppliers and the difference between the highest marginal cost and the buyer’s reservation price are sufficiently large, each supplier can gain a higher profit if the marginal costs are private information. On the contrary, when the highest marginal cost approaches the buyer’s reservation price, complete cost information benefits the suppliers.     

Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach

Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a manufacturer–retailer supply chain contemporaneously. By means of game theory, four different relationships between the channel members are considered: Firstly, three non-cooperative games with either symmetrical distribution of power or asymmetrical distribution with one player being the leader in each case, and one cooperative game where both players tend to maximize the total profit. The latter is complemented by a bargaining model, which proposes a fair split of profit on the basis of the players’ risk attitude and bargaining power. Our main findings are as follows: (a) In contrast to previous analyses, we do not limit the ratio between manufacturer’s and retailer’s margin, which provides more general insights into the effects of the underlying distribution of power within the channel. (b) The highest total profit is gained when both players cooperate. This behavior puts also the customers in a better position, as it produces the lowest retail price as well as the highest advertising expenditures compared to the other configurations.     

Technology selection and capacity investment under uncertainty

We analyze the problem of technology selection and capacity investment for electricity generation in a competitive environment under uncertainty. Adopting a Nash-Cournot competition model, we consider the marginal cost as the uncertain parameter, although the results can be easily generalized to other sources of uncertainty such as a load curve. In the model, firms make three different decisions: (i) the portfolio of technologies, (ii) each technology’s capacity and (iii) the technology’s production level for every scenario. The decisions related to the portfolio and capacity are ex-ante and the production level is ex-post to the realization of uncertainty. We discuss open and closed-loop models, with the aim to understand the relationship between different technologies’ cost structures and the portfolio of generation technologies adopted by firms in equilibrium. For a competitive setting, to the best of our knowledge, this paper is the first not only to explicitly discuss the relation between costs and generation portfolio but also to allow firms to choose a portfolio of technologies. We show that portfolio diversification arises even with risk-neutral firms and technologies with different cost expectations. We also investigate conditions on the probability and cost under which different equilibria of the game arise.     

Suppliers’ competition and manufacturer’s product mix: the role of ingredient brand

This paper proposes a pricing game among a manufacturer and two competing suppliers. One of the suppliers establishes an ingredient brand, which can enhance the valuations of the end products. The equilibrium is derived to investigate the impact of the ingredient brand awareness and the production costs on the suppliers’ pricing competition, the manufacturer’s product mix and retail price(s), and profits. The result shows that the manufacturer may provide unique product or differentiated products, depending on the effectiveness of ingredient branding strategy. We distinguish two different monopolistic scenarios in supplier market and provide the condition for each supplier to survive. We find that the ingredient branding strategy mitigates the pricing competition between suppliers and benefits the manufacturer in a low production cost industry.     

On the cooperation of recycling operations

This paper addresses two important issues that may affect the operations efficiency in the recycling industry. First, the industry contains many small-scale and inefficient recycling firms, especially in developing countries. Second, the output from recycling a waste product often yields multiple recycled products that cannot all be sold efficiently by a single firm. To address these two issues, this paper examines how different firms can cooperate in their recycling and pricing decisions using cooperative game theory. Recycling operations under both joint and individual productions with different cost structures are considered. Decisions include the quantity of waste product to recycle and the price at which to sell each recycled product on each firm’s market. These decisions can be made jointly by multiple cooperating firms to maximize total profit. We design allocation schemes for maximized total profit to encourage cooperation among all firms. Managerial insights are provided from both environmental and economic perspectives.     

Coordinating ordering and pricing decisions in a two-stage distribution system with price-sensitive demand through short-term discounting

We consider a short-term discounting model in which the distributor offers a discounted price for the retailers’ orders placed at the beginning of its replenishment cycle, in a non-cooperative distribution system with one distributor and multiple retailers, each facing price-sensitive demand. We examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers’ ordering and pricing decisions under two common types of demand, linear demand in price and constant elasticity demand in price. Our numerical study reveals that, in the presence of homogeneous retailers (namely, retailers with identical demand rates), the distributor’s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases, but increases as price elasticity increases. Although an increase in the inventory holding cost rate has a negative effect on the distributor’s profit, it may have a positive effect on the retailers’ profits. We further find that with heterogeneous retailers (namely, retailers with different demand rates), offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large. This cross effect, however, is absent under constant elasticity demand.     

Price and lead time decisions in dual-channel supply chains

Manufacturers today are increasingly adopting a dual channel to sell their products, i.e., the traditional retail channel and an online direct channel. Empirical studies have shown that service quality (we focus on the delivery lead time of the direct channel) even goes beyond product price as one of the major factors influencing consumer acceptance of the direct channel. Delivery lead time has significant effects on demand, profit, and pricing strategy. However, there is scant literature addressing the decision on the promised delivery lead time of a direct channel and its impact on the manufacturer’s and retailer’s pricing decisions. To fill this gap, we examine the optimal decisions of delivery lead time and prices in a centralized and a decentralized dual-channel supply chain using the two-stage optimization technique and Stackelberg game, and analyze the impacts of delivery lead time and customer acceptance of a direct channel on the manufacturer’s and retailer’s pricing behaviours. We analytically show that delivery lead time strongly influences the manufacturer’s and the retailer’s pricing strategies and profits. Our numerical studies reveal that the difference between the demand transfer ratios in the two channels with respect to delivery lead time and direct sale price, customer acceptance of the direct channel, and product type have great effects on the lead time and pricing decisions.     

Coordinating pricing and production decisions in the presence of price competition

In this paper we study the effects of coordinating pricing and production decisions on the improvement of a firm’s position in a price-competitive environment. Assuming duopolistic market conditions, we use game-theoretic concepts and models to analyze two scenarios. A firm’s marketing and production departments may vertically coordinate their pricing and production quantity decisions and the two firms may horizontally compete for price-sensitive random demand. The two scenarios include (i) no coordination and (ii) coordination in both firms. We show that by coordinating their pricing and production decisions, competing firms can increase their profitability—especially when conditions are unfavourable (i.e., with smaller market sizes, higher unit costs and lower unit revenues). While it may be intuitive to expect that coordination will outperform non-coordination, our models provide a means for formalizing and quantifying the differences between the two policies.     

A two-stage supply chain coordination mechanism considering price sensitive demand and quantity discounts

This paper explores the coordination between a supplier and a buyer within a decentralized supply chain, through the use of quantity discounts in a game theoretic model. Within this model, the players face inventory and pricing decisions. We propose both cooperative and non-cooperative approaches considering that the product traded experiences a price sensitive demand. In the first case, we study the dynamics of the game from the supplier's side as the leader in the negotiation obtaining a Stackelberg equilibrium, and then show how the payoff of this player could still improve from this point. In the second case, a cooperative model is formulated, where decisions are taken simultaneously, emulating a centralized firm, showing the benefits of the cooperation between the players. We further formulate a pricing game, where the buyer is allowed to set different prices to the final customer as a reaction to the supplier's discount decisions. For the latter we investigate the difference between feasibility of implementing a retail discount given a current coordination mechanism and without it. Finally the implications of transportation costs are analyzed in the quantity discount schedule. Our findings are illustrated with a numerical example showing the difference in the players’ payoff in each case and the optimal strategies, comparing in each case our results with existing work.     

A capacitated firm’s pricing strategies for strategic consumers with different search costs

This paper studies pricing strategies of a seller with budget constraints facing two types of strategic consumers with different search costs, and proposes three pricing strategies to motivate all consumers to visit his shop. These are the basic price strategy, differentiated compensation strategy and an improved differentiated compensation strategy. Based on the rational expectations paradigm, we characterize the rational expectations equilibrium in the game and propose a basic pricing strategy. In order to address the interplay between price and demand, we further propose a differentiated compensation strategy to improve the basic model. We then compare the differentiated compensation strategy to the basic pricing strategy when both are feasible. We find that selection of the optimal strategy is independent of composition of consumers but is dependent on the seller’s budget level and the difference between the two search costs. If the budget is large enough and the difference between the search costs is small enough, a differentiated compensation strategy can further improve the seller’s profitability. In addition to these findings, we first propose an improved differentiated compensation strategy to further enhance the firm’s profit. We find that the optimal strategy is to implement the improved differentiated compensation strategy when all three strategies are feasible. Interestingly, the firm may benefit from paying a high compensation to the consumers.     

Periodicity of pricing and marketing efforts in a distribution channel

Most research about cooperative (coop) advertising programs in channels relies on the assumption that manufacturers and retailers decide of pricing and marketing efforts simultaneously. This paper evaluates this central assumption and investigates the optimal periodicity (sequence of move) of pricing and marketing efforts (ME) decisions for a distribution channel. We develop a game theoretic model that accounts for pricing at each level of the channel, for the manufacturer’s ME mix strategies (a direct ME to consumers and coop advertising program offered to the retailer) and the retailer’s ME as well. We obtain solutions for a bilateral channel under different vertical interaction scenarios; when the channel is led by the manufacturer, the retailer or when channel members decide simultaneously of each of their marketing mix decisions (vertical Nash). We compare the effect of pricing and ME decision periodicity on outputs for each channel member. The main findings suggest that simultaneous decision-making of pricing and ME is optimal only for high enough levels of the manufacturer’s ME effects. For very highly effective marketing efforts, sequential play of pricing and ME allows channel members to implement equilibrium strategies and achieve maximum profits that would not be achieved with simultaneous decision-making. This highlights the importance of relaxing the simultaneous play assumption of pricing and ME in a distribution channel.     

Non-cooperative joint replenishment under asymmetric information

We consider jointly replenishing n ex-ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exists and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm’s type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs.     

Spatial competition and collaboration networks

We model the formation of collaboration networks among firms that are located in a circular city as a two-stage game. In the first stage, the firms form collaboration links, and in the second stage, they engage in price competition. If two firms form a link, their production costs in the second stage are reduced. The second stage is a generalization of Salop??s (Bell J Econ 10(1):141?C156, 1979) circular city model. We provide a complete characterization of equilibrium prices of the model. We show that a firm prefers forming a link with a more distant firm if the cost-reducing effects are the same. We discuss the stability and social efficiency of the collaboration networks. When link costs are small, there is no conflict between efficiency and stability of networks. When link costs are significant, there is a conflict between efficiency and stability of networks. We also examine the average distances between linked firms.     

Lead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games

In a firm, potential conflict exists between manufacturing and sales departments. Salespersons prefer to order from manufacturing departments in advance so that they can secure products in the amount they need to satisfy customers in time. This time in advance strategy is defined as “lead-time hedging.” While this hedging strategy is good for the sales department to guarantee the right quantity at the right time for customers, it adds additional costs and pressure to the manufacturing department. One scheme to resolve this conflict is to introduce a fair “internal price,” charged by the manufacturing department to the sales department. In this paper, two models involving a fair internal price are introduced. In one model, a Nash game is played to reach an optimal strategy for both parties. In the other model, a Stackelberg game is played in which the manufacturing department serves as the leader. We show that these two models can successfully reduce lead-time hedging determined by the salesperson and can increase the firm’s overall profit, as compared to the traditional model without considering the internal price. More insights have also been analyzed that include the comparisons of the manufacturer’s and the salesperson’s profits among the traditional model, the Nash game model, the Stackelberg game model, and the centralized global optimization model.     

Dynamic Bertrand Oligopoly

We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash equilibrium when there are N players with heterogeneous costs. In the dynamic game with uncertain market demand, firms of different sizes have different lifetime capacities which deplete over time according to the market demand for their good. We setup the nonzero-sum stochastic differential game and its associated system of HJB partial differential equations in the case of linear demand functions. We characterize certain qualitative features of the game using an asymptotic approximation in the limit of small competition. The equilibrium of the game is further studied using numerical solutions. We find that consumers benefit the most when a market is structured with many firms of the same relative size producing highly substitutable goods. However, a large degree of substitutability does not always lead to large drops in price, for example when two firms have a large difference in their size.     

Approximating Nash equilibrium for production control with sticky price

We study a mean field game problem arising from the production control for multiple firms with price stickiness in the commodity market. The price dynamics for each firm is described as a (controlled) jump-diffusion process with mean-field interaction. Each firm aims to maximize her expectation of cumulative net profit coupled with each other through price processes. By solving the limiting control problem and a fixed-point problem, we construct an explicit approximating Nash equilibrium when the number of firms grows large.