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.     

具有产品质量差异的扩展Hotelling模型

假定两家厂商生产的同种产品具有质量差异,及消费者对产品质量偏好服从[d,e]区间上的均匀分布情况,研究了二次运输成本Hotelling模型:两家厂商首先沿[0,1]线性城市同时选址,然后进行价格竞争.运用后退归纳法得到了子博弈精炼Nash均衡,此时厂商将选址于城市中心。     

Hotelling’s location model with negative network externalities

We study a variation of Hotelling’s location model in which consumers choose between firms based on travel distances as well as the number of consumers visiting each firm. The model in which the network externality is the same for all firms was proposed by Kohlberg (Econ Lett 11:211–216, 1983), who claims that no equilibrium exists for more than two firms. We assume the network effects to be linear and, in contrast to the claim in Kohlberg (Econ Lett 11:211–216, 1983), derive a condition under which a subgame perfect Nash equilibrium exists for four and six firms. Moreover, we show that for more than two firms the equilibrium locations of the firms are different from the equilibrium locations in Hotelling’s location model. Our results suggest that a subgame perfect Nash equilibrium exists if and only if the number of firms is even. We also provide examples of subgame perfect equilibria in which the network externality is different for some of the firms.     

Finding all pure strategy Nash equilibria in a planar location game

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.     

双寡头时间限制型免费试用策略竞争分析

目前,提供限时免费试用已经成为软件厂商降低消费者对产品质量不确定性及促进新产品扩散的常见做法。现有研究多局限于垄断情况,对现实中常出现的寡头竞争情况鲜有探讨。在考虑消费者学习异质性的基础上,基于Hotelling模型研究了双寡头企业免费试用策略博弈均衡及其影响因素。结果表明:(1)如果两家企业的期望用户体验都比较好,都应该提供免费试用;如果期望用户体验都比较差,都不提供。(2)否则,均衡结果进一步取决于消费者对他们之间水平差异的敏感性。如果很不敏感,则两家企业必须采取相反的免费试用提供策略,并且只有当它们的期望用户体验差距很大时,优势企业一定提供而劣势企业不提供;否则,保持相反即可。如果非常敏感,则两家企业只需在免费试用提供策略上保持一致即可。(3)消费者完全学习软件所需时间越长,两家企业“都不提供”和“只需一致”的可能性增大,而“都提供”和“必定相反”的可能性降低。这是对免费试用策略竞争问题进行的首次探索,所得结果对相关理论研究具有补充和促进作用,也能为相关实践提供科学的决策依据。     

Duopoly information sharing with differentiated products

Consider a model where firms own the same technology in linear Cournot duopolies with differentiated products and the slope of the demand curve facing the firm is unknown, containing an own-price effect and a cross-effect. We discuss as follows: whether there is an incentive to share information when firms are symmetrically informed about the random demand. In a two-stage game, for independent goods and complements, it is a Nash equilibrium for firms to put their private information in a common pool.     

Finding location equilibria for competing firms under delivered pricing

We address the problem of finding location equilibria of a location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. Assuming that firms set the equilibrium prices in the second stage, the game is reduced to a location game for which a global minimizer of the social cost is a location equilibrium if demand is completely inelastic and marginal production cost is constant. The problem of social cost minimization is studied for both a network and a discrete location space. A node optimality property when the location space is a network is shown and an Integer Linear Programming (ILP) formulation is obtained to minimize the social cost. It is also shown that multiple location equilibria can be found if marginal delivered costs are equal for all competitors. Two ILP formulations are given to select one of such equilibria that take into account the aggregated profit and an equity criterion, respectively. An illustrative example with real data is solved and some conclusions are presented.     

Strategic multi-store opening under financial constraint

This paper analyzes strategic store openings in a situation in which firms can open multiple stores depending on the financial constraints of the firm. Specifically, given any upper limit of the number of store openings that two potentially symmetric firms can open, they sequentially determine the number of store openings, including their locations, to maximize their profits. As a result of our analysis in a microeconomic framework, we show that the equilibrium strategy can be wholly classified into only two following opposite strategies according to the level of their financial constraints involved. When firms can afford to invest significant amounts of money in the market, the leader chooses “segmentation strategy,” in which a part of the market can be monopolized by opening a chain of multiple stores and deterring the follower’s entry. In contrast, when the leader has a severe financial constraint so that it can only monopolize less than half of the market, the leader chooses “minimum differentiation strategy,” where firms open each of their stores at exactly the same point as the rival’s. Under this strategy, the leader necessarily captures just half of the market. Furthermore, we show that regardless of potential symmetry between firms, both first and second mover advantages in terms of profit can occur in the equilibrium.     

Stocking and quality decisions for deteriorating perishable products under competition

In this study, we address the joint inventory and quality management in a Cournot duopoly, for a seasonally produced, perishable product whose quality deteriorates over time. The sales of the product occur over two periods, namely the season (first period) and the off-season (second period). Apart from the stocking quantities for the two periods, firms must decide the quality levels of the units to stock for the second selling period. Firms incur a cost to maintain particular quality levels. The equilibrium policies of the firms are characterized, and we discuss the impact of the firms’ quality costs on their inventory and quality decisions. We identify the conditions of the quality costs when competition ceases to exist in the second period, and analyse the impact of the quality costs on inter-temporal price fluctuations and product availability. Using the unconstrained equilibrium policy, we frame the firms’ inventory disposal policies when production yields are exogenous.     

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.     

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.     

Cournot competition with hyperbolic learning and myopic firms: A note

In this note, we provide a Cournot oligopoly model of learning-by-doing that incorporates both learning spillovers and organizational forgetting, relaxing the commonly made assumption of linear learning by considering a hyperbolic learning curve that depends on both own and rivals’ experience. The analysis is conducted under the assumption of myopic firms. We show that conditions exist under which more competition, captured by an increase in the number of firms, worsens both productive and allocative efficiency at the steady-state equilibrium.     

Symmetric equilibrium with random entry

This paper considers Cournot-Nash equilibrium with free entry among identical firms which possess large minimum efficient scale. We consider equilibrium in which all firms receive equal treatment by allowing firms to play mixed strategies. In particular, firms randomize over the decision to enter or not. It is shown that symmetric Cournot-Nash equilibrium in mixed strategies exists when there is a finite number of potential entrants. We then consider a sequence of such mixed strategy equilibria as the number of potential entrants gets large. It is shown that such a sequence always has a convergent subsequence whose limit is a symmetric equilibrium in mixed strategies when the number of potential entrants is infinite. An example is given which shows that increased competition, in the form of a larger pool of potential entrants, is socially harmful in that expected social surplus is decreasing in the number of potential entrants.     

Game Options Analysis of the Information Role of Call Policies in Convertible Bonds

Abstract

In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm.     

Nonlinear Cournot oligopoly games with isoelastic demand function: The effects of different behavior rules

The analysis of asymptotical convergence for the oligopoly game has always been important to characterize the firms’ long-term behavior. In the nonlinear oligopoly competition possibly involving chaotic fluctuations, non-convergent trajectories are particularly undesirable since the resulting behavior will become unpredictable. In this paper, consistent with a traditional assumption that the firms update their outputs simultaneously, we at first construct an adjustment process and discuss the convergence to the equilibrium for a nonlinear Cournot duopoly game with the isoelastic demand function. We indicate that the tendency to instability does rise with the number of firms and the adjustment speeds. In particular, we alter this assumption from simultaneous decisions to sequential decisions so that the latter firms are able to observe the former ones at every time periods. We finally arrive at a conclusion that the unique equilibrium is convergent as long as the adjustment speeds are less than a fixed threshold, no matter what the number of the firms. Our findings show that the firms with sequential decisions can achieve the equilibrium more easily.     

Corporate governance and firm performance: Evidence from Japanese manufacturing industries after the lost decade

This study investigates whether a series of recent economic reforms on corporate governance influence the operational performance of Japanese manufacturing industries after the bubble economy. This study finds that stable shareholding is an important aspect of traditional Japanese corporate governance. Many Japanese corporate leaders still believe that the stable shareholders are important for their governance. However, the stable shareholding enhances their operational performance only when the ratio of shares held by stable shareholders is more than 61.21%. This result is inconsistent with the previous governance strategy of Japanese management. Moreover, the foreign investment enhances the operational performance of Japanese firms until the ratio of shares held by foreign shareholders becomes 19.49%. Japanese corporate leaders are very afraid of the foreign investment. This result is inconsistent with their opinions, as well. The second result indicates that Japanese firms need to accept more foreign investment and pay attention to the opinion of foreign investors. Finally, it is important for Japanese firms to make a balance between the traditional stable shareholding and the foreign investment.     

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.     

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.     

Capacity competition of make-to-order firms

Two make-to-order firms, each modelled as a single-server queue, compete for a common stream of (potential) customers by setting their service capacities (rates) and service prices. Each customer maximizes her expected return by getting service from a firm or by balking. We completely characterize the Nash equilibrium of the competition.     

On bargaining partner selection when communication is restricted

This paper analyzes the optimal selection of a bargaining partner when communication among players is restricted by an exogenously given graph. If players are equally patient, bargaining agreements are immune to players' locations, and the selection of a bargaining partner is not an issue. In contrast, when players differ in their discount factors, both location and impatience matter for bilateral agreements and partner selection becomes an issue. We show that selecting the most impatient neighbor is an equilibrium strategy whenever two players having a common neighbor share their most impatient neighbor. This condition is always satisfied by stratified graphs with no more than three strata. In the absence of this condition, cyclically-stratified graphs with no more than three strata also admit this equilibrium selection rule. Received: November 2000/Final version: January 2002