Efficiency Analysis of Cournot Competition in Service Industries with Congestion

We consider Cournot competition in the presence of congestion effects. Our model consists of several service providers with differentiated services, each competing for users who are sensitive to both price and congestion. We distinguish two types of congestion effects, depending on whether spillover costs exist, that is, where one service provider's congestion cost increases with the other providers' output level. We quantify the efficiency of an unregulated oligopoly with respect to the optimal social welfare with tight upper and lower bounds. We show that, when there is no spillover, the welfare loss in an unregulated oligopoly is limited to 25% of the social optimum, even in the presence of highly convex costs. On the other hand, when spillover cost is present, there does not exist a constant lower bound on the efficiency of an unregulated oligopoly, even with affine cost. We show that the efficiency depends on the relative magnitude between the marginal spillover cost and the marginal benefit to consumers

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis and that agents can choose only pure strategies, we identify a structural condition on the preference b(x,y) of agent type x for product type y -- and on the principal's costs c(y) -- which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal's problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal's optimum strategy -- and similarly of the strategy maximizing the expected welfare of the agents when the principal's profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang's necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.Comment: 23 page

Price of anarchy in supply chains, congested systems and joint ventures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-174).This thesis studies the price of anarchy in supply chains, congested systems and joint ventures. It consists of three main parts. In the first part, we investigate the impact of imperfect competition with nonlinear demand. We focus on a distribution channel with a single supplier and multiple downstream retailers. To evaluate the performance, we consider several metrics, including market penetration, total profit, social welfare and rent extraction. We quantify the performance with tight upper and lower bounds. We show that with substitutes, while competition improves the efficiency of a decentralized supply chain, the asymmetry among the retailers deteriorates the performance. The reverse happens when retailers carry complements. We also show that efficiency of a supply chain with concave (convex) demand is higher (lower) than that with affine demand. The second part of the thesis studies the impact of congestion in an oligopoly by incorporating convex costs. Costs could be fully self-contained or have a spillover component, which depends on others' output. We show that when costs are fully self-contained, the welfare loss in an oligopoly is at most 25% of the social optimum, even in the presence of highly convex costs. With spillover cost, the performance of an oligopoly depends on the relative magnitude of spillover cost to the marginal benefit to consumers. In particular, when spillover cost outweighs the marginal benefit, the welfare loss could be arbitrarily bad. The third part of the thesis focuses on capacity planning with resource pooling in joint ventures under demand uncertainties. We distinguish heterogeneous and homogeneous resource pooling. When resources are heterogeneous, the effective capacity in a joint venture is constrained by the minimum individual contribution. We show that there exists a unique constant marginal revenue sharing scheme which induces the same outcome in a Nash equilibrium, Nash Bargaining and the system optimum. The optimal scheme rewards every participant proportionally with respect to his marginal cost. When resources are homogeneous, we show that the revenue sharing ratio should be inversely proportional to a participant's marginal cost.by Wei Sun.Ph.D

Monotone Comparative Statics for Equilibrium Problems

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems, monotone comparative statics, and results on the structure of the core of matching games without transfers (Gale and Shapley) and with transfers (Demange and Gale). More specifically, we introduce the notions of 'unified gross substitutes' and 'nonreversingness' and show that if Q is a supply correspondence defined on a set of prices P which is a sublattice of R^N, and Q satisfies these two properties, then the set of prices yielding supply vector q is increasing (in the strong set order) in q; and it is a sublattice of P

Dynamic pricing with demand learning under competition

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 199-204).In this thesis, we focus on oligopolistic markets for a single perishable product, where firms compete by setting prices (Bertrand competition) or by allocating quantities (Cournot competition) dynamically over a finite selling horizon. The price-demand relationship is modeled as a parametric function, whose parameters are unknown, but learned through a data driven approach. The market can be either in disequilibrium or in equilibrium. In disequilibrium, we consider simultaneously two forms of learning for the firm: (i) learning of its optimal pricing (resp. allocation) strategy, given its belief regarding its competitors' strategy; (ii) learning the parameters in the price-demand relationship. In equilibrium, each firm seeks to learn the parameters in the price-demand relationship for itself and its competitors, given that prices (resp. quantities) are in equilibrium. In this thesis, we first study the dynamic pricing (resp. allocation) problem when the parameters in the price-demand relationship are known. We then address the dynamic pricing (resp. allocation) problem with learning of the parameters in the price-demand relationship. We show that the problem can be formulated as a bilevel program in disequilibrium and as a Mathematical Program with Equilibrium Constraints (MPECs) in equilibrium. Using results from variational inequalities, bilevel programming and MPECs, we prove that learning the optimal strategies as well as the parameters, is achieved. Furthermore, we design a solution method for efficiently solving the problem. We prove convergence of this method analytically and discuss various insights through a computational study.(cont.) Finally, we consider closed-loop strategies in a duopoly market when demand is stochastic. Unlike open-loop policies (such policies are computed once and for all at the beginning of the time horizon), closed loop policies are computed at each time period, so that the firm can take advantage of having observed the past random disturbances in the market. In a closed-loop setting, subgame perfect equilibrium is the relevant notion of equilibrium. We investigate the existence and uniqueness of a subgame perfect equilibrium strategy, as well as approximations of the problem in order to be able to compute such policies more efficiently.by Carine Simon.Ph.D

Three Essays on Pricing and Risk Management in Industrial Practice.

In this dissertation, I study three types of uncertainties in industrial practice: the demand uncertainty, the earnings uncertainty and the external market uncertainty. In particular, Chapter 2 prices the demand uncertainties in the just-in-time (JIT) outsourcing between an original equipment manufacturer (OEM) and a contract manufacturer (CM) with flexible production capacity. Under this JIT outsourcing arrangement, the OEM transfers uncertain market demand to the CM without explicitly compensating the latter for the cost due to demand risks. I propose a model that prices the CM's cost of bearing this demand risk and the OEM's benefit of transferring it. I show that when the outsourcing demand is positively correlated with the either party's existing business, the higher risk it carries, the more it benefits the OEM and costs the CM. Chapter 3 proposes a model for a managed print services (MPS) provider to manage his earnings uncertainties by selecting contract terms. MPS is the unified management over institutional customers’ hardcopy device fleets. Using a proprietary dataset of Xerox, I study the optimal contracts from a risk-averse provider’s perspective. On the customer's side, I demonstrate that the customer's printing demand is insensitive to service prices. Furthermore, I show that a linear model can adequately characterize the customer's service payments. Using this linear model as an input, I build an optimization model that yields the optimal contracts that minimize the provider’s earnings variability while maximizing the expected earnings. Finally, I provide empirical evidence that the provider is better modeled as being risk-averse rather than risk-neutral. Chapter 4 aims to understand the uncertainties of the external market trends and market responses using resale prices of a particular type of used durable goods. I identify the market trends within each functionality segment, across the industry, and within each brand and OEM. I observe that the external market trends capture up to 81.4% of the volatility of an arbitrary product’s resale price, indicating strong comovements among different products. I also show there is no material impact on product resale prices due to brand termination. A big product recall, however, results in significant product price drops.PhDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100031/1/jien_1.pd

Demand Effects in Productivity and Efficiency Analysis

Demand fluctuations will bias the measurement of productivity and efficiency. This dissertation described three ways to characterize the effect of demand fluctuations. First, a two-dimensional efficiency decomposition (2DED) of profitability is proposed for manufacturing, service, or hybrid production systems to account for the demand effect. The first dimension identifies four components of efficiency: capacity design, demand generation, operations, and demand consumption, using Network Data Envelopment Analysis (Network DEA). The second dimension decomposes the efficiency measures and integrates them into a profitability efficiency framework. Thus, each component's profitability change can be analyzed based on technical efficiency change, scale efficiency change and allocative efficiency change. Second, this study proposes a proactive DEA model to account for demand fluctuations and proposes input or output adjustments to maximize effective production. Demand fluctuations lead to variations in the output levels affecting measures of technical efficiency. In the short-run, firms can adjust their variable resources to address the demand fluctuates and perform more efficiently. Proactive DEA is a short-run capacity planning method, proposed to provide decision support to a firm interested in improving the effectiveness of a production system under demand uncertainty using a stochastic programming DEA (SPDEA) approach. This method improves the decision making related to short-run capacity expansion and estimates the expected value of effectiveness given demand. In the third part of the dissertation, a Nash-Cournot equilibrium is identified for an oligopolistic market. The standard assumption in the efficiency literature that firms desire to produce on the production frontier may not hold in an oligopolistic market where the production decisions of all firms will determine the market price, i.e. an increase in a firm's output level leads to a lower market clearing price and potentially-lower profits. Models for both the production possibility set and the inverse demand function are used to identify a Nash-Cournot equilibrium and improvement targets which may not be on the strongly efficient production frontier. This behavior is referred to as rational inefficiency because the firm reduces its productivity levels in order to increase profits

Provably near-optimal algorithms for multi-stage stochastic optimization models in operations management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-165).Many if not most of the core problems studied in operations management fall into the category of multi-stage stochastic optimization models, whereby one considers multiple, often correlated decisions to optimize a particular objective function under uncertainty on the system evolution over the future horizon. Unfortunately, computing the optimal policies is usually computationally intractable due to curse of dimensionality. This thesis is focused on providing provably near-optimal and tractable policies for some of these challenging models arising in the context of inventory control, capacity planning and revenue management; specifically, on the design of approximation algorithms that admit worst-case performance guarantees. In the first chapter, we develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The proposed policies have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. We also describe a 6-approximation algorithm for the counterpart model under uniform capacity constraints. In the second chapter, we study a class of revenue management problems in systems with reusable resources and advanced reservations. A simple control policy called the class selection policy (CSP) is proposed based on solving a knapsack-type linear program (LP). We show that the CSP and its variants perform provably near-optimal in the Halfin- Whitt regime. The analysis is based on modeling the problem as loss network systems with advanced reservations. In particular, asymptotic upper bounds on the blocking probabilities are derived. In the third chapter, we examine the problem of capacity planning in joint ventures to meet stochastic demand in a newsvendor-type setting. When resources are heterogeneous, there exists a unique revenue-sharing contract such that the corresponding Nash Bargaining Solution, the Strong Nash Equilibrium, and the system optimal solution coincide. The optimal scheme rewards every participant proportionally to her marginal cost. When resources are homogeneous, there does not exist a revenue-sharing scheme which induces the system optimum. Nonetheless, we propose provably good revenue-sharing contracts which suggests that the reward should be inversely proportional to the marginal cost of each participant.by Cong Shi.Ph.D