Equilibrium two-part cost structures

We consider an oligopolistic product market in which two competing firms instead of paying a competitive input price choose a two-part tariff. Costs for the input are divided up into upfront fixed costs independent of the output level and reductions in marginal costs. We explore under which competitive settings will such a two-part cost structure correspond to equilibrium behavior in a two stage game. We find that firms in a static model do have an incentive to choose a two-part cost structure when competition in the product market is not too strong and oligopoly rents can be shifted form the rival to the own firm. In a dynamic market when firms use Markov strategies competition is so intense that there are no rents to be shifted and firms do not benefit from two-part cost structures.     

Collaboration and sharing mechanisms in improving corporate social responsibility

This paper investigates the effects of the collaboration between an upstream and a downstream firm regarding their decisions of prices and levels of corporate social responsibility (CSR) efforts. The firms collaborate with each other by sharing their costs or benefits to improve their profitabilities and CSR performances. Three collaborative models are developed for considering that collaboration may be undertaken by either or both firms, and each model has both profit- and cost-sharing mechanisms. We derive and characterize the consumer valuation and the firms’ decisions at equilibrium with respect to the changes in the sharing scheme, and further identify the impacts of each sharing mechanism. Moreover, a Nash bargaining game is developed for examining the choices of sharing scheme under the negotiation between the firms. Finally, we provide economic and managerial insights for socially concerned companies.     

Co-authorship model with link strength

We generalize a network formation model for co-authorship introducing the possibility of the connections having different link strengths. Different link strengths represent the fact that authors may put different efforts into different collaborations. To evaluate the model, we consider the notions of efficiency and pairwise stability, which are based on a utility function that measures the benefits for an author to belonging to a certain network structure. We divide the analysis in two cases, considering that link strengths are unbounded or bounded. In the first case, we show that if there are more than two authors in the network, then there is no pairwise stable network. In the second case, we show that the pairwise stable networks consist of completely connected disjoint components where essentially all link strengths are maximal. Regarding efficiency, in both cases, if the number of authors is even, then the unique efficient network structure consists of pairs of connected authors.     

Price competition in the Hotelling model with uncertainty on costs

For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of incomplete information in the production costs of both firms. We introduce the bounded uncertain costs (BUC) condition in the production costs and we prove that there is a local optimum price strategy if and only if the BUC condition holds. We compute explicitly the local optimum price strategy and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We prove that the ex-post profit of a firm is smaller than its ex-ante profit if and only if the production cost of the other firm is greater than its expected cost.     

Less-Than-Truckload carrier collaboration problem: modeling framework and solution approach

Less-Than-Truckload (LTL) carriers generally serve geographical regions that are more localized than the inter-city line-hauls served by truckload carriers. That localization can lead to urban freight transportation routes that overlap. If trucks are traveling with less than full loads, there typically exist opportunities for carriers to collaborate over such routes. We introduce a two stage framework for LTL carrier collaboration. Our first stage involves collaboration between multiple carriers at the entrance to the city and can be formulated as a vehicle routing problem with time windows (VRPTW). We employ guided local search for solving this VRPTW. The second stage involves collaboration between carriers at transshipment facilities while executing their routes identified in phase one. For solving the second stage problem, we develop novel local search heuristics, one of which leverages integer programming to efficiently explore the union of neighborhoods defined by new problem-specific move operators. Our computational results indicate that integrating integer programming with local search results in at least an order of magnitude speed up in the second stage problem. We also perform sensitivity analysis to assess the benefits from collaboration. Our results indicate that distance savings of 7–15 % can be achieved by collaborating at the entrance to the city. Carriers involved in intra-city collaboration can further save 3–15 % in total distance traveled, and also reduce their overall route times.     

Surplus division and investment incentives in supply chains: A biform-game analysis

In this paper, we use a biform-game approach for analyzing the impact of surplus division in supply chains on investment incentives. In the first stage of the game, firms decide non-cooperatively on investments. In the second stage, the surplus is shared according to the Shapley value. We find that all firms have inefficiently low investment incentives which, however, depend on their position in the supply chain. Cross-subsidies for investment costs can mitigate, but not eliminate the underinvestment problem. Vertical integration between at least some firms.yields efficient investments, but may nevertheless reduce the aggregated payoff of the firms. We show how the size of our effects depends on the structure of the supply chain and the efficiency of the investment technology. Various extensions demonstrate that our results are qualitatively robust.     

Signaling advertising by multiproduct firms

We consider the use of advertising expenses as quality signals in multiproduct firms, extending previous results on single product firms. In our model, a firm introduces sequentially two products whose qualities are positively correlated. We investigate whether there exist information spillovers from the first to the second market. We show that, when correlation is high, the equilibrium in market 2 depends on the quality reputation the firm has gained in market 1. Moreover, if a firm with a high-quality product 1 wants to separate from its low-quality counterpart, it needs to advertise more in this market than if the qualities of the two products are unrelated. This advertising level signals not only high quality in the first market, but also the likely quality of the second product. Thus, advertising in the first market has information spillovers in the second market.     

Asymmetric dynamic price competition with uncertainty

We consider a dynamic setting-price duopoly model in which a dominant (leader) firm moves first and a subordinate (follower) firm moves second. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms, for different values of the intercept demand parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal trading and shipping of agricultural commodities

We develop and implement a model for a profit maximizing firm that provides an intermediation service between commodity producers and commodity end-users. We are motivated by the grain intermediation business at Los Grobo—one of the largest commodity-trading firms in South America. Producers and end-users are distributed over a realistic spatial network, and trade with the firm through contracts for delivery of grain during the marketing season. The firm owns spatially distributed storage facilities, and begins the marketing season with a portfolio of prearranged purchase and sale contracts with upstream and downstream counterparts. The firm aims to maximize profits while satisfying all previous commitments, possibly through the execution of new transactions. Under realistic constraints for capacities, network structure and shipping costs, we identify the optimal trading, storing and shipping policy for the firm as the solution of a profit-maximizing optimization problem, encoded as a minimum cost flow problem in a time-expanded network that captures both geography and time. We perform extensive numerical examples and show significant efficiency gains derived from the joint planning of logistics and trading.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

A leader-follower model and analysis for a two-stage network of oligopolies

This paper is concerned with the existence, uniqueness and computation of leader-follower equilibrium solutions for an industry involved with two major stages of production. We assume that there exists one set of firms performing the first stage of production, which produces a semi-finished product. This semi-finished product is converted to a final good by a second set of firms performing the second stage of production. Furthermore, also competing in the final product market is a third set of firms, which are vertically integrated through the two stages of production and which are assumed to lead the second set of firms by explicitly considering the reaction or response of these latter firms to their own outputs. We model such an industry as a two-stage network of oligopolies, and define equilibrium solutions based on assumed market structures. Our analysis examines the existence and uniqueness of such equilibrium solutions, characterizes the nature of the production strategies of the various firms at an equilibrium, and prescribes algorithms to compute such solutions. This provides the machinery required to perform sensitivity analyses for studying the effects of various mergers or integrations on individual firm profits, and on the industry outputs and prices at equilibrium. The presentation is self-contained, and does not necessarily require any significant prior preparation in economic theory on the part of the reader.This paper is based on work done for the Minerals and Mining Resources Research Institute, under the sponsorship of the Bureau of Mines, Department of the Interior.     

The impact of cost uncertainty on the location of a distribution center

The location of a distribution center (DC) is a key consideration for the design of supply chain networks. When deciding on it, firms usually allow for transportation costs, but not supplier prices. We consider simultaneously the location of a DC and the choice of suppliers offering different, possibly random, prices for a single product. A buying firm attempts to minimize the sum of the price charged by a chosen supplier, and inbound and outbound transportation costs. No costs are incurred for switching suppliers. We first derive a closed-form optimal location for the case of a demand-populated unit line between two suppliers offering deterministic prices. We then let one of the two suppliers offer a random price. If the price follows a symmetric and unimodal distribution, the optimal location is closer to the supplier with a lower mean price. We also show the dominance of high variability: the buyer can decrease the total cost more for higher price variability for any location. The dominance result holds for normal, uniform, and gamma distributions. We propose an extended model with more than two suppliers on a plane and show that the dominance result still holds. From numerical examples for a line and a plane, we observe that an optimal location gets closer to the center of gravity of demands as the variability of any supplier’s price increases.     

Equilibrium Pricing and Advertising Strategies in a Marketing Channel

This paper is concerned with conflict and coordination in a two-member channel of distribution. We propose a differential game model that includes carryover effects of advertising, expressed by a retailer-specific stock of advertising goodwill. Pricing and advertising strategies for both firms are identified under channel conflict as well as coordination. Dynamic advertising policies are designed as stationary Markov perfect strategies. In a symmetric case, these strategies can be determined in closed form, taking into consideration explicitly nonnegativity constraints on advertising rates. We establish a global result for the relationship between the advertising strategies of the two firms under conflict and coordination.     

Decentralized job matching

This paper studies a multi-stage decentralized matching model where firms sequentially propose their (unique) positions to workers. At each stage workers sequentially decide which offer to accept (if any). A firm whose offer has been declined may make an offer to another worker in the next stage. The game stops when all firms either have been matched to a worker or have already made unsuccessful offers to any worker remaining in the market. We show that there is a unique subgame-perfect equilibrium outcome, the worker-optimal matching. Firms in this game have a weakly dominant strategy, which consists of making offers in the same order as given by their preferences. When workers play simultaneously any stable matching can be obtained as an equilibrium outcome, but an unstable matching can obtain in equilibrium.     

A game-theoretic analysis of information sharing and security investment for complementary firms

This paper investigates information sharing and security investments by two firms provided that their information assets are complementary in the sense that their combined information assets are of significant value, whereas the information asset of a single firm is no value to an attacker. In particular, assuming that each firm chooses its security investment and information sharing individually, we obtain some insights about the optimal choices for the firms and the attacker, which form sharp comparisons with those derived from common (substitutive) firms. We further analyse the effect of a social planner on social total costs by assuming that it can control security investments, information sharing and both of them respectively. We demonstrate that an increase in intervention by the social planner may not necessarily be preferable.     

Coalition formation of oligopolistic firms for information exchange

This paper investigates the coalition formation of oligopolistic firms for exchanges of information about their cost functions in a game-theoretical framework. An oligopolistic market under uncertainty is considered in which each firm knows its own cost function but not those of all the others. The following results are shown. It is profitable for each firm to exchange the information about cost functions with other firms. When the uncertainty levels of the cost functions of all firms are symmetric. it is common interest for them to exchange their information by forming the grand coalition. On the other hand, when their uncertainty levels are highly asymmetric, firms possessing less uncertain cost functions come into conflict with one another when exchanging information exclusively with the most uncertain firms. As a result, more than one coalition may be formed among firms.     

Investment and financing decisions in the presence of time-to-build

We study a firm’s optimal decisions on investment, default, and financing when the amount of time and the running costs for project completion are uncertain. In the presence of time-to-build, a firm makes conservative investment and financing decisions; investment is delayed, and the optimal leverage ratio is inverted U-shaped with respect to the size of the lag. Although equity holders can choose to default before the project has been completed, the default probability in the presence of time-to-build is lower than that in the absence of a lag in most cases because of the conservative investment and financing decisions. Given the lower default probability, equity holders may benefit more from debt financing in the presence of time-to-build than they would in the absence of a lag. When firms can shorten their expected time-to-build by bearing more costs, unlevered firms strive to reduce the lag more than optimally levered firms do. However, highly levered firms utilize more resources to reduce the lag than all-equity firms do because equity holders are more concerned about the possibility of default before the project’s completion.     

A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.     

Environmental considerations on the optimal product mix

Several types of regulations limit the amount of different emissions that a firm may create from its production processes. Depending on the emission, these regulations could include threshold values, penalties and taxes, and/or emission allowances that can be traded. However, many firms try to comply with these regulations without a systematic plan, often leading not only to emission violations and high penalties, but also to high costs. In this paper, we present two mathematical models that can be used by firms to determine their optimal product mix and production quantities in the presence of several different types of environmental constraints, in addition to typical production constraints. Both models are comprehensive and incorporate several diverse production and environmental issues. The first model, which assumes that each product has just one operating procedure, is a linear program while the second model, which assumes that the firm has the option of producing each product using more than one operating procedure, is a mixed integer linear program. The solutions of both models identify the products that the firm should produce along with their production quantities. These models can be used by firms to quickly analyze several “what if” scenarios such as the impact of changes in emission threshold values, emission taxes, trading allowances, and trading transaction costs.     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.