Dynamic Monopoly Research Articles

Quality Is in the Eye of the Beholder: Taste Projection in Markets with Observational Learning

We study how misperceptions of others’ tastes influence beliefs, demand, and prices in markets with observational learning. Consumers infer a good’s quality from the quantity demanded and price paid by others. When consumers exaggerate the similarity between their and others’ tastes, such “taste projection” generates discrepant quality perceptions, which are decreasing in a projector’s taste and increasing in the observed price. These biased inferences produce an excessively elastic market demand. We also analyze dynamic monopoly pricing with short-lived taste-projecting consumers. Optimal pricing follows a declining path: a high initial price inflates future buyers’ perceptions, and lower subsequent prices induce overadoption. (JEL D42, D83, D91, L15)

Quid Pro Quo CSR and Trade Liberalization in a Bilateral Monopoly

We construct a dynamic bilateral monopoly game to analyze the bargaining between a foreign manufacturer and a domestic retailer regarding the wholesale price and explain the foreign upstream firm’s corporate social responsibility (CSR) initiative and its economic impacts on the domestic market. Under free trade, the foreign upstream firm’s CSR initiative realizes improvements in consumer surplus and social welfare in the home country. A “win–win–win” strategy exists, as the foreign manufacturer has more of an incentive to implement CSR when the government implements a strategic trade policy. The consumer-friendly action implemented by the foreign upstream firm leads to adequate consumer welfare and social welfare, which mitigates the government’s political hostility. With the high bargaining power of the foreign upstream firm and the low weight of the consumer-friendly upstream firm, the government should set a higher tariff rate for the foreign upstream firm to extract rent and enhance social welfare.

Dynamic monopoly and consumers profiling accuracy

AbstractUsing a Markov‐perfect equilibrium model, we show that the use of customer data to practice intertemporal price discrimination will improve monopoly profit if and only if information precision is higher than a certain threshold level. This U‐shaped relationship lends support to a popular view that knowledge is good only if it is sufficiently refined. When information accuracy can only be achieved through costly investment, we find that investing in profiling is profitable only if this allows to reach a high enough level of information precision. Consumers expected surplus being a hump‐shaped function of information accuracy, we show that consumers have an incentive to lobby for privacy protection legislation which raises the cost of monopoly's investment in information accuracy. However, this cost should not dissuade firms to collect some information on customers' tastes, as the absence of consumers' profiling is actually detrimental to consumers.

Quality improvement and process innovation of a firm facing reference price effects in a dynamic monopoly

ABSTRACT In this article, we investigate a monopolist’s efforts for product innovation (or quality improvement) and process innovation (or reducing marginal production cost) with reference price effects in a dynamic setting. The significant features of our work are: (i) a monopolist deals with customer behavior according to economic principles and determines the price of the product, besides, the monopolist carries out the activities of product and process innovation; (ii) the consumers’ demand structure depends on product price, product quality and reference price, and takes a separable multiplicative way between the state variables (product quality and reference price) and the control variables (product price). Our main results suggest that (i) there exists unique saddle-point steady-state equilibrium under monopoly and social planning; (ii) as the memory parameter increases, it is very likely that the monopolist’s steady-state effort for process innovation is greater than that for product innovation; (iii) the efforts for product and process innovation under social planning are greater than that under monopoly; (iv) although the price is still determined by the monopolist under the social planning, the price under the social planning is higher than that under monopoly and (v) there is a negative price-quality relationship.

On the spread of influence in graphs

Consider a graph G and an initial configuration where each node is black or white. Assume that in each round all nodes simultaneously update their color based on a predefined rule. In the r-threshold (resp. α-threshold) model, a node becomes black if at least r of its neighbors (resp. α fraction of its neighbors) are black, and white otherwise.A node set D is said to be a dynamic monopoly if black color takes over once all nodes in D are black. We provide several tight bounds on the minimum size of a dynamic monopoly in terms of different graph parameters. Furthermore, we prove some bounds on the stabilization time of the process. Finally, we also establish bounds on the minimum size of a dynamic monopoly and the stabilization time in the aforementioned models, as a function of the underlying graph's expansion.

A Note on the Majority Dynamics in Inhomogeneous Random Graphs

In this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete graph K_n independently with probability p_n(e). Each vertex is independently assigned an initial state +1 (with probability p_+) or -1 (with probability 1-p_+), updated at each time step following the majority of its neighbors’ states. Under some regularity and density conditions of the edge probability sequence, if p_+ is smaller than a threshold, then G will display a unanimous state -1 asymptotically almost surely, meaning that the probability of reaching consensus tends to one as nrightarrow infty . The consensus reaching process has a clear difference in terms of the initial state assignment probability: In a dense random graph p_+ can be near a half, while in a sparse random graph p_+ has to be vanishing. The size of a dynamic monopoly in G is also discussed.

Facets of the dynamic monopoly polytope: Linear ordering formulation

We study the polyhedral structure of the monopoly polytope which arises from an integer programming formulation of dynamic monopolies in graphs. This formulation extends from the linear ordering polytope formulation. Several families of valid and facet defining inequalities are investigated. We show that (anti-) arborescences lead to families of strong valid inequalities each of which contains exponentially many facet defining inequalities. We also generalize the k-fence and Möbius ladder inequalities for the monopoly polytope.

Dynamic Monopoly and Consumers Profiling Accuracy

Using a Markov-perfect equilibrium model, we show that the use of customer data to practice intertemporal price discrimination will improve monopoly profit if and only if information precision is higher than a certain threshold level. This U-shaped relationship lends support to a popular view that knowledge is good only if it is sufficiently refined. When information accuracy can only be achieved through costly investment, we find that investing in profiling is profitable only if this allows to reach a high enough level of information precision. Consumers expected surplus being a hump-shaped function of information accuracy, we show that consumers have an incentive to lobby for privacy protection legislation which raises the cost of monopoly’s investment in information accuracy. However, this cost should not dissuade firms to collect some information on customers’ tastes, as the absence of consumers’ profiling is actually detrimental to consumers.

Informational Robustness in Intertemporal Pricing

Abstract We introduce a robust approach to study dynamic monopoly pricing of a durable good in the face of buyer learning. A buyer receives information about her willingness-to-pay for the seller’s product over time, and decides when to make a one-time purchase. The seller does not know how the buyer learns but commits to a pricing strategy to maximize profits against the worst-case information arrival process. We show that a constant price path delivers the robustly optimal profit, with profit and price both lower than under known values. Thus, under the robust objective, intertemporal incentives do not arise at the optimum, despite the possibility for information arrival to influence the timing of purchases. We delineate whether constant prices remain optimal (or not) when the seller seeks robustness against a subset of information arrival processes. As part of the analysis, we develop new techniques to study dynamic Bayesian persuasion.

Knowledge Transfer, Transitional Dynamics and Optimal Research & Development Policy in a Dynamic Monopoly Setting

This paper focuses on the question of whether or not a reduction of the knowledge barrier is good for welfare. Based on a dynamic monopoly setting with simultaneous investment decisions in process as well as in product Research & Development (R&D), we show that a reduction of the knowledge barrier has ambiguous welfare consequences: due to a lower knowledge barrier, product quality and welfare increase in the short-run. However, this may not necessarily be the case in the long-run. One reason is that a positive long-lasting knowledge barrier shock triggers the monopolist sub-optimally to reduce its product R&D investments today and in the future at the cost of future product quality. This in turn may reduce welfare. Accordingly, to realize the first-best level of product quality, the long-run optimal R&D subsidy rate for product innovations increases with a reduction of the knowledge barrier.

Quality and price personalization under customer recognition: A dynamic monopoly model with contrasting equilibria

We present a model of market hyper-segmentation, where a monopolist acquires within a short time all information about the preferences of consumers who purchase its vertically differentiated products. The firm offers a new price/quality schedule after each commitment period. Lower consumer types may have an incentive to delay their purchases until next period to obtain a better introductory offer. The monopolist counters this incentive by offering higher informational rents. Considering the dynamic game played by the monopolist and its customers, we find that there is always a Markov perfect equilibrium (MPE) in which the firm immediately sells the good to all customers, offering the Mussa–Rosen static equilibrium schedule to first time customers (and getting full commitment profits). However, if the commitment period between two offers is long enough, there is another MPE with gradual market expansion. Contrary to the Coasian result for a durable-good monopoly, we find that in both equilibria the profit of the monopolist increases (and the aggregate consumers surplus decreases) as the interval of commitment shrinks. The model yields policy implications for regulations on collection and storage of customers information.

Partial immunization of trees

For a graph G and a non-negative integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent lower and upper bounds, and fixing the total increase. We solve this problem efficiently for trees, which extends a result of Khoshkhah and Zaker (2015).

Quality and Price Personalization under Customer Recognition: a Dynamic Monopoly Model

We present a model of market hyper-segmentation, where a monopolist acquires within a short time all information about the preferences of consumers who purchase its vertically differentiated products within a given period. The firrm offers a new price/quality schedule after each commitment period. Lower consumer types may have an incentive to delay their purchases until next period to obtain a better introductory offer to new customers. The monopolist counters this incentive by offering higher informational rents. Considering the dynamic game played by the monopolist and its customers, we find that there is always a Markov perfect equilibrium (MPE) in which the firm immediately sells the good to all its customers, offering the Mussa-Rosen static equilibrium schedule to first time customers (and getting full commitment profits). However, if the commitment period between two offers is long enough, there is another MPE, where the number of customers that are served expands only gradually. Contrary to the Coasian result for a durable-good monopoly, we find that in both equilibria the profit of the monopolist increases (and the consumers' expected surplus decreases) as the interval of commitment shrinks. The model yields policy implications for regulation on information collection and commitment period.

On some tractable and hard instances for partial incentives and target set selection

A widely studied model for influence diffusion in socialnetworks are target sets. For a graph G and an integer-valued threshold function τ on its vertex set, a target set or dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the entire vertex set of G. This notion is limited to the binary choice of including a vertex in the target set or not, and Cordasco, Gargano, Rescigno, and Vaccaro proposed partial incentives as a variant allowing for intermediate choices.We show that finding optimal partial incentives is hard for chordal graphs and planar graphs but tractable for graphs of bounded treewidth and for interval graphs with bounded thresholds. We also contribute some new results about target set selection on planar graphs by showing the hardness of this problem, and by describing an efficient O(n)-approximation algorithm as well as a PTAS for the dual problem of finding a maximum degenerate set.

Dynamic monopolies for interval graphs with bounded thresholds

For a graph G and an integer-valued threshold function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. It is known that the problem of finding a dynamic monopoly of minimum order is NP-hard for split graphs. We show that this problem can be solved in polynomial time for interval graphs with bounded threshold functions.

A polyhedral study of dynamic monopolies

Spread of influence in a network can be modeled and studied within the concept of dynamic monopolies in graphs. We give an integer programming formulation for finding a minimum dynamic monopoly in an undirected graph. The corresponding 0–1 polytope and its facets are studied and several families of facet defining inequalities are introduced. Computational experiments have been performed to show the strength of the IP formulation and its facet defining inequalities.

Vaccinate your trees!

For a graph G and an integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We study two vaccination problems, where the goal is to maximize the minimum order of such a dynamic monopoly•either by increasing the threshold value of b vertices beyond their degrees,•or by removing b vertices from G, where b is a given non-negative integer corresponding to a budget. We show how to solve these problems efficiently for trees.

A dynamic monopoly with risk-averse consumers

I study the dynamically optimal pricing strategy of a forward-looking monopolist that introduces a novel product when facing a normalized population of risk-averse, non-strategic consumers. The product can be seen as an experience good in the first period. How well the product fits the consumers’ taste is learned only after experimentation, allowing for signaling in the second period. I find that the larger the degree of risk aversion, the higher the probability of observing an introductory price. Moreover, after the realization of a relatively poor fit between the product and the consumers’ taste, an introductory price is optimal from an ex-post perspective. Finally, a first-period price ceiling leads to a strictly larger level of welfare if and only if consumers are moderately risk averse.

Learning quality through prices and word‐of‐mouth communication

AbstractThis paper studies the effect of word‐of‐mouth communication on the optimal pricing strategy for new experience goods. I consider a dynamic monopoly model with asymmetric information about product quality, in which consumers learn in equilibrium from both prices and other consumers. The main result is that word‐of‐mouth communication is essential for the existence of separating equilibria, wherein the high‐quality monopolist signals high quality through a low introductory price (lower than the monopoly price), and the low‐quality one charges the monopoly price. The intuition is simple: low prices are costly, and will only be used by firms confident enough that increased experimentation (and therefore communication among consumers) will yield good news about quality and increased future profits. Additional results are the following: for the high‐quality seller, the expected price (quantity) is increasing (decreasing) over time; whereas for the low‐quality one, the opposite is true. Moreover, signaling becomes more difficult when consumers pay less attention to their peers' reports and more attention to past prices. Finally, word‐of‐mouth communication improves consumer welfare.

Tax and Welfare in Dynamic Monopoly

This paper studies the role of taxation in durable good markets with dynamic monopolies. By conditioning the marginal tax rate on the volume of trade, the regulator can provide incentives for the monopolist to accelerate trade. When marginal cost pricing is incentive-feasible, tax policy with back-loaded subsidy can induce the first-best allocation with budget neutrality. When marginal cost pricing generates a loss for the monopolist, strategic delay cannot be avoided under regulatory budget constraint. Reducing delay then requires different forms of tax policy depending on the monopolist's commitment power. In particular, without commitment, front-loaded subsidy improves welfare.