A note on price and quality competition between asymmetric firms

This paper analyzes the impact of asymmetry between firms on the outcome of price and quality competition from a microeconomic viewpoint. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. The asymmetry arises from the difference in consumers’ loyalty to each firm; that asymmetry then determines a character of differentiation between firms. Our purpose is to show how asymmetry influences competition under varying consumers’ price- and quality-sensitivity. In doing so, we extend earlier work in the area of price and quality competition. We show that in both the moderately quality-sensitive and price-sensitive markets, higher consumers’ sensitivity as well as lower consumers’ loyalty to any firm leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. On the other hand, in highly quality-sensitive market, asymmetry compels the smaller firm to change its competitive strategy. In general, this is more beneficial to the larger firm, as the smaller firm’s profit tends to decline. In the worst case, the smaller firm is driven out of business under equilibrium.     

Consumer environmental awareness and competition in two-stage supply chains

This paper focuses on the impact of competition and consumers’ environmental awareness on key supply chain players. We consider both the production competition between partially substitutable products made by different manufacturers, and the competition between retail stores. We use two-stage Stackelberg game models to investigate the dynamics between the supply chain players given three supply chain network structures. We find that as consumers’ environmental awareness increases, retailers and manufacturers with superior eco-friendly operations will benefit; while the profitability of the inferior eco-friendly firm will tend to increase if the production competition level is low, and will tend to decrease if the production competition level is high. In addition, higher levels of retail competition may make manufacturers with inferior eco-friendly operations more likely to benefit from the increase of consumers’ environmental awareness. Moreover, as production competition intensifies, the profits of the retailers will always increase, while the profits of the manufacturers with inferior eco-friendly operations will always decrease. The profitability of the manufacturers with superior eco-friendly operations will also tend to decrease, unless consumers’ environmental awareness is high and the superior manufacturer has a significant cost advantage related to product environmental improvement.     

Willingness-to-pay estimation with choice-based conjoint analysis: Addressing extreme response behavior with individually adapted designs

The increasing consideration of behavioral aspects in operations management models has prompted greater use of choice-based conjoint (CBC) studies in operations research. Such studies can elicit consumers’ willingness to pay (WTP), a core input for many optimization models. However, optimization models can yield valid results only if consumers’ WTP is estimated accurately. A simulation study and two field studies show that extreme response behavior in CBC studies, such that consumers always or never choose the no-purchase option, harms the validity of WTP estimates. Reporting the share of consumers who always and never select the no-purchase option allows for detecting extreme response behavior. This study suggests an individually adapted design that avoids extreme response behavior and thus significantly improves WTP estimation accuracy.     

Using MSRP to enhance the ability of rebates to control distribution channels

Manufacturers have increasingly instituted widespread mail-in rebate programs in recent years. Two primary purposes for rebates are to: (1) more directly impact consumer demand by reducing net retail price, and (2) capitalize on consumers’ slippage behavior because not all consumers who intend to redeem the rebate at purchase time end up actually redeeming it. However, retailers can counteract the power of rebates to impact demand by simply raising the retail price by the amount of the manufacturer’s rebate. We show that by combining a manufacturer’s suggested retail price (MSRP) along with a rebate, the manufacturer can better control the channel by inhibiting the retailer’s ability to raise price, particularly when consumers exhibit loss aversion. As a result, incorporating MSRP with a rebate promotion plan increases the manufacturer’s profit. More surprisingly, the profit of the supply chain as a whole also increases, and the channel efficiency increases as well. In fact, contrary to results from the existing rebate literature suggesting that rebates should always be offered whenever slippage exists, we demonstrate that MSRP can actually be a more effective tool than rebates in managing retailer and consumer behavior when consumers do not have sufficient loss aversion and the slippage rate is low enough.     

QoS commitment between vertically integrated autonomous systems

Vertically integrated autonomous systems bargain to provide quality of service guarantees and revenue sharing. Depending on the perceived quality of service and access price, consumers determine whether they subscribe to the access provider’s service. Four types of contracts are compared: (i) best effort, (ii) bilateral bargaining, (iii) cascade negotiations and (iv) grand coalition cooperation; the impact of the consumers’ QoS sensitivity parameter and power relation are tested for each contract. Assuming that the consumers’ quality of service sensitivity parameter is unknown and might evolve dynamically due to error judgement, word-of-mouth effect or competition pressure, a learning algorithm is detailed and implemented by each integrated autonomous systems under asymmetrical information. Its convergence and the influence of bias introduction by the most informed autonomous system is analyzed.     

Farsighted stable sets in Hotelling’s location games

We apply the farsighted stable set to two versions of Hotelling’s location games: one with a linear market and another with a circular market. It is shown that there always exists a farsighted stable set in both games, which consists of location profiles that yield equal payoff to all players. This stable set contains location profiles that reflect minimum differentiation as well as those profiles that reflect local monopoly. These results are in contrast to those obtained in the literature that use some variant of Nash equilibrium. While this stable set is unique when the number of players is two, uniqueness no longer holds for both models when the number of players is at least three.     

Distributed consensus in noncooperative inventory games

This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a consensus protocol that allows the convergence of the players’ strategies to the Pareto optimal Nash equilibrium. The protocol allows each player to construct its belief by exchanging only some aggregate but sufficient information with a restricted number of neighbor players. Such a networked information structure has the advantages of being scalable to systems with a large number of players and of reducing each player’s data exposure to the competitors.     

Analysis of the effectiveness of manufacturer-sponsored retailer gift cards in supply chains

Some manufacturers sponsor “free” retailer gift cards to be given to consumers who purchase their products. These gift cards are paid for by the manufacturer and are redeemable on all products at the retailer. We develop a model of such a supply chain. We analyze cases in which the gift cards’ redemption rate is constant or increasing in gift card value. The results indicate that in addition to the redemption rate and consumers’ valuation for gift card dollars, the profitability of manufacturer-sponsored gift cards depends on the average gross margin of the retailer and the type of purchases consumers make with gift cards. Furthermore, we show that under certain conditions, free gift cards will increase the expected profits of the retailer and manufacturer as well as decrease the retail price of the product. These conditions include a retailer with large average gross margin and consumers using gift cards to purchase products they would not buy with cash otherwise. Furthermore, all consumers, including those who do not redeem the gift card, are more likely to benefit from a reduced retail price when their probability of redeeming the gift card after purchase is equal to their estimated redemption probability at purchase time. We show the conditions under which gift cards are more profitable than cash mail-in rebates. We develop an incentive scheme to improve the performance of supply chains with gift cards.     

Competitive facility location on decentralized supply chains

This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.     

On competitive sequential location in a network with a decreasing demand intensity

We introduce and analyze a Hotelling like game wherein players can locate in a city, at a fixed cost, according to an exogenously given order. Demand intensity is assumed to be strictly decreasing in distance and players locate in the city as long as it is profitable for them to do so. For a linear city (i) we explicitly determine the number of players who will locate in equilibrium, (ii) we fully characterize and compute the unique family of equilibrium locations, and (iii) we show that players’ equilibrium expected profits decline in their position in the order. Our results are then extended to a city represented by an undirected weighted graph whose edge lengths are not too small and co-location on nodes of the graph is not permitted. Further, we compare the equilibrium outcomes with the optimal policy of a monopolist who faces an identical problem and who needs to decide upon the number of stores to open and their locations in the city so as to maximize total profit.     

Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.     

Average shadow price and equilibrium price: A case study of tradable pollution permit markets

Shadow prices indicate implicit values of limited resources at the margin and provide important information in decision making for resource management. In continuous economic models, shadow prices associated with demand-supply balance constraints represent consumers’ willingness to pay and producers’ marginal cost, hence they correspond to market equilibrium prices. As well known, however, marginal analysis fails in the case of discrete optimization, such as mixed integer programming. An alternative concept has been introduced in the literature to measure the value of an extra unit of a limited resource in such cases. This concept is based on average rather than marginal values, thus called the average shadow price, and interpreted in the same way as conventional shadow prices. Whether average shadow prices in a discrete economic model can serve as market equilibrium prices has not been addressed in the related literature. The present paper addresses this issue in an empirical setting. Using a tradable pollution permit market as an example, where firms’ YES/NO type technology adoption decisions are represented by binary variables, we show that the average shadow price of tradable permits can be interpreted as the equilibrium price only when certain conditions related to the cost structure and emission levels hold. On the other hand, we show that an iterative procedure based on individual firms’ cost minimizing behavior presents a better approach for finding a price that can eliminate or reduce the gap between demand and supply of permits in the market.     

Customization competition between branded firms: Continuous extension of product line from core product

We study a competition of product customization between two branded firms by a game-theoretic approach. Firms produce products with two attributes: one attribute indicates a characteristic with regard to “function” or “design” of a product and the other indicates “taste” or “flavor” of the product, which reflects consumers’ brand/taste preferences. Two branded firms have their own specific core products and our customization is defined as a continuous extension of their product line from the core product only along the “function” attribute. In particular, we allow asymmetric positions of core products, which may create the position advantage/disadvantage between firms. We suppose that consumers incur their selection costs with regard to finding their most favorable item among a rich variety of products and firms incur their customizing costs with regard to extending their product lines. We first show that in the equilibrium, branded firms should fundamentally adopt their customizations to cover the center space in the market as far as possible, regardless of the position of the competitor’s core product. Therefore, the position of the core product contributes to the creation of a competitive advantage: when one firm’s core product is located more closely to the center of the market than the competitor’s, its customization can always cover more range of the center space in the market, while keeping its degree of customization smaller than the competitor’s. Furthermore, we show some implications of unit-cost improvement: in a short run, a firm is better off concentrating on the improvement of the unit selection cost rather than the unit customizing cost. In contrast, in a long run, both firms can benefit from the improvement of the unit customizing cost.     

Full-line or specialization strategy? The negative effect of product variety on product line strategy

This paper studies the product line decisions of firms under two consumer segments differing in their quality-sensitivity. We focus on a negative impact of the product variety on the consumers’ motivation to purchase, while each product is horizontally differentiated. In the presence of this impact and high fixed costs relative to variable costs, it is shown that when a highly quality-sensitive segment exists, it is always advantageous for the monopoly to specialize in only one product serving this segment. However, the appearance of a competitor can drastically change the product line in the market. Under the duopolistic setting where two firms sequentially determine their product lines, we show that the leader gains a better financial result by offering its product to the low segment for many cases, including the case where no product is offered to the high segment by either of the firms who are in equilibrium. Furthermore, we obtain another interesting result that indicates that the follower’s profit can exceed the leader’s profit when the quality-sensitivities between the two consumer segments are sufficiently different, even though the two firms are symmetric except for the order of their product offerings.     

Pricing and effort investment for a newsvendor-type product

We investigate a dominant retailer’s optimal joint strategy of pricing and timing of effort investment and analyze how it influences the decision of the manufacturer, the total supply chain profit, and the consumers’ payoff. We consider two pricing schemes of the retailer, namely, dollar markup and percentage markup, and two effort-investment sequences, namely, ex-ante and ex-post. A combination of four cases is analyzed. Our results show that: (1) under the same effort-decision sequence, a percentage-markup pricing scheme leads to higher expected profit for the retailer and the whole supply chain, but a lower expected profit for the manufacturer and a higher retail price for the consumers; (2) under the same markup-pricing strategy, the dominant retailer always prefers to postpone her effort decision until the manufacturer makes a commitment to wholesale price, since it can result in a Pareto-improvement for all the supply chain members. That is, the retailer’s and manufacturer’s expected profits are higher and the consumers pay a lower retail price; and (3) among the four joint strategies, the dominant retailer always prefers the joint strategy of percentage-markup plus ex-post effort decision. However, the dominated manufacturer always prefers the joint strategy of dollar-markup plus ex-post effort decision, which is also beneficial to the end consumers.     

Online retailers’ promotional pricing,free-shipping threshold,and inventory decisions: A simulation-based analysis

We consider a two-stage decision problem, in which an online retailer first makes optimal decisions on his profit margin and free-shipping threshold, and then determines his inventory level. We start by developing the retailer’s expected profit function. Then, we use publicly-available statistics to find the best-fitting distribution for consumers’ purchase amounts and the best-fitting function for conversion rate (i.e., probability that an arriving visitor places an online order with the retailer). We show that: (i) a reduction of the profit margin does not significantly affect the standard deviation of consumers’ order sizes (purchase amounts) but increases the average order size; whereas, (ii) variations in a positive finite free-shipping threshold affect both the average value and the standard deviation of the order sizes. We then use Arena to simulate the online retailing system and OptQuest to find the retailer’s optimal decisions and maximum profit. Next, we perform a sensitivity analysis to examine the impact of the ratio of the unit holding and salvage cost to the unit shipping cost on the retailer’s optimal decisions. We also draw some important managerial insights.     

Congestion games with failures

We introduce a new class of games, congestion games with failures (CGFs), which allows for resource failures in congestion games. In a CGF, players share a common set of resources (service providers), where each service provider (SP) may fail with some known probability (that may be constant or depend on the congestion on the resource). For reliability reasons, a player may choose a subset of the SPs in order to try and perform his task. The cost of a player for utilizing any SP is a function of the total number of players using this SP. A main feature of this setting is that the cost for a player for successful completion of his task is the minimum of the costs of his successful attempts. We show that although CGFs do not, in general, admit a (generalized ordinal) potential function and the finite improvement property (and thus are not isomorphic to congestion games), they always possess a pure strategy Nash equilibrium. Moreover, every best reply dynamics converges to an equilibrium in any given CGF, and the SPs’ congestion experienced in different equilibria is (almost) unique. Furthermore, we provide an efficient procedure for computing a pure strategy equilibrium in CGFs and show that every best equilibrium (one minimizing the sum of the players’ disutilities) is semi-strong. Finally, for the subclass of symmetric CGFs we give a constructive characterization of best and worst equilibria.     

Robust game theory

We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our ``robust game' model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call ``robust-optimization equilibrium,' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results. The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the Singapore-MIT Alliance. The research of the author was partially supported by the Singapore-MIT Alliance.     

Supply chain structure in a market with deceptive counterfeits

Deceptive counterfeits differ from non-deceptive ones in that they are packaged and sold as authentic brand name products so that consumers may buy counterfeits unknowingly. When a distribution channel, referred to as the general channel, has been penetrated with deceptive counterfeits, a brand name company may need to restructure the way its products are distributed and rely on reliable channels such as certified stores or manufacturer-owned stores to guarantee 100% authenticity. In this paper, we first identify the conditions under which the general channel will carry deceptive counterfeits, and then analyze the optimal supply chain structure in the presence of counterfeits as well as by incorporating the wholesale price decisions, consumers’ risk attitude towards counterfeits and consumer loyalty towards the reliable stores. Our main finding is that the brand name company should continue to sell, sometimes exclusively, through the general channel despite deceptive counterfeiting under various conditions.     

Existence of equilibria in a decentralized two-level supply chain

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.