New product introduction and capacity investment by incumbents: Effects of size on strategy

We analyze a duopoly where capacity-constrained firms offer an established product and have the option to offer an additional new and differentiated product. We show that the firm with the smaller capacity on the established market has a higher incentive to innovate and reaches a larger market share on the market for the new product. An increase in capacity of the larger firm can prevent its competitor from innovating, whereas an increase in capacity of the smaller firm cannot prevent innovation of its larger competitor. In equilibrium the firm with smaller capacity on the established market might outperform the larger firm with respect to total payoffs.     

Patent-investment games under asymmetric information

This paper analyzes preemptive patenting in a two-stage real options game where an incumbent firm competes with a potential entrant firm for the patent of a substitute product in a product market with profit flow uncertainty. The incumbent suffers loss of monopoly in the product market if the entrant acquires the patent of a substitute product and later commercializes the product. Our patent-investment game model assumes that the entrant has complete information on the incumbent’s commercialization cost while the incumbent only knows the distribution of the entrant’s cost. We investigate the impact of information asymmetry on the preemption strategies adopted by the two competing firms on patenting the substitute product by comparing the optimal preemption strategies and the real option value functions of the two competing firms under complete information and information asymmetry. Our analysis reveals that the informationally disadvantaged incumbent always suffers from loss in its real option value of investment since it tends to act more aggressively in competing for the patent. On the other hand, the real option value of investment of the informationally advantaged entrant may be undermined or enhanced. The incumbent’s aggressive response under information asymmetry may lead to reversal of winner in the patent race. We also examine how information asymmetry may affect the occurrence of sleeping patent and the corresponding expected duration between the two stages of patenting and product commercialization.     

A Computational Model of Technological Innovation at the Firm Level

The factors which speed and slow technological innovation have been of interest to policy makers since at least the mid 1960's. Since that time, many theoretical models of innovation at the firm level and at the industry level have been proposed. Due to limitations in computational complexity, nearly all of these models have assumed a single, representative firm type. Very few have systematically investigated the implications of markets with a variety of firm types. With increases in computing power and the advent of agent-based modeling, interactions between agent types can now be explored. In this paper, a computational model of innovative firms in competitive markets is presented. Firms devote resources to R&D which can lead to new, improved products allowing firms to steal market share from their competitors. Two types of firms, differentiated by the strategies they use in pursuing new innovations, are allowed to coexist. One type pursues exclusively radical innovations, while the other pursues exclusively incremental innovations. It will be demonstrated that under certain conditions, a synergy exists between firms of different types which allows heterogeneous populations of firms to earn more than homogeneous ones.     

高维市场结构与创新

以往的创新研究局限于一维市场结构：所有企业的创新能力都一样，谁也不占有优势。实际上应根据企业不同的创新能力特征，分成若干种类型，形成高维市场结构，在此结构下研究创新竞争。本首先证明在高维市场结构下均衡点唯一；其次指出何种类型企业具有竞争优势，分析企业合资研究对竞争优势的影响；最后讨论竞争企业数量增加时均衡状态的变化，并将市场的结果与社会最优结果作比较。     

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.     

非对称情形下R & D竞争项目的策略性投资

在非对称情形下,考虑具有技术不确定和未来收益不确定的竞争研究与开发(R&;D)项目的不可逆策略性投资.利用期权博弈理论和随机优化方法给出了高效研发公司(主导者) 的最优投资阈值和最优投资规则的解析表达式,并证明了由于两公司的竞争使投资阈值下降.其次讨论了两公司的混合投资策略,并给出每个公司执行投资期权的概率和两公司同时执行投资期权的概率. 在最后给出了数值模拟算例来说明该文结论的合理性.     

Strategic upfront marketing channel integration as an entry barrier

This paper investigates an organizational design problem concerning whether duopolistic firms competing in a product market should vertically integrate or separate their marketing channels in a dynamic noncooperative game setting. Previous operational research models have shown that the separation of the marketing channel with the adoption of a two-part tariff contract is the dominant strategy compared with integration for each firm if the two firms face retail price competition, and thereby constitutes the subgame perfect Nash equilibrium (SPNE). Contrary to this previous insight, this paper demonstrates that if exogenous parameters that characterize fixed costs, product substitutability, and a demand function fall into a specific region, marketing channel integration dominates the separation strategy when one of the two firms is the incumbent firm while the other is a potential entrant. In other words, the well-known result in the price-setting game can be reversed when we take entry threats into consideration. Specifically, we show that upfront vertical integration of the marketing channel enables the incumbent to deter the entry of the potential competitor and to monopolize the market in the SPNE. This result has operational implications for a firm confronting the threat of potential rivals entering the market, in that the firm can use this apparently inferior strategy as a commitment device, which creates a virtual entry barrier.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

医药产学研联盟创新决策、创新危机与利润分配

以我国医药行业产学研合作创新为现实背景,构建两家相互竞争的制药企业与学研机构的双边纳什议价模型,分析企业的创新价值和议价能力对联盟成员绩效的影响,探讨合作创新对药品价格、企业市场份额、经营绩效和社会福利的影响,研究制药企业创新战略的选择决策及创新对企业可能的危险。通过模型分析,得到如下结论:产学研合作创新能够提高社会总福利,但不一定提高制药企业的绩效和药品的价格;议价能力强的制药企业不一定总是获得高利润,企业最终的利润受到企业自身及竞争者的议价能力、创新价值的共同影响;虽然产品创新能够提高消费者的购买意愿,但盲目跟风创新可能会带来双输的结果。本研究对促进医药行业的产学研合作,提高产学研合作的有效性具有现实意义。     

The impact of product recall on advertising decisions and firm profit while envisioning crisis or being hazard myopic

The occurrence of a product recall can have a disastrous effect on the firm responsible for the recall. Any major recall by a firm can negatively affect the goodwill of the firm. Consequently, the firm incurs a substantial indirect cost due to decline in sales and loss in profit. Moreover, a competitor’s opportunistic reaction can intensify the recalling firm’s damages. Strategic use of advertising recovers lost goodwill and mitigates the damages made by a product recall. In this paper, using a goodwill based model under a differential game framework, we analyze the equilibrium strategies of two competing manufacturers when either one firm or both can issue a product recall at a random time, and investigate (i) the firms’ equilibrium advertising strategies (ii) analyze the impact of the recall on a firm’s profit (iii) introduce and investigate the effect of “hazard myopia” (a firm’s inability to foresee the crisis likelihood) on a firm’s advertising decisions and profit. Our study finds that the equilibrium advertising strategies of competing firms depend on the impact and likelihood of the recall. Notably, we find that when both the firms are focal firms without the prior knowledge of who will recall first in a planning horizon, adjusting optimal advertising at an appropriate time is essential. Surprisingly, a product-recall with a minor impact can increase the focal firm’s long-term expected profit. On the other hand, hazard myopia can be profitable if the long-term effect of the recall is small. Our findings suggest that advertising levels of firms should differ in pre-recall and post-recall regimes depending on the impact and likelihood of the recall.     

Optimal production in a competitive market under yield uncertainty

Motivated by the U.S. influenza vaccine market, we study the impact of random yield and production capacity on the number of firms, total supply, consumer surplus and social welfare in a market with identical suppliers. We formulate a two-stage game with endogenous entry, where each entering firm aims to maximize its profit under yield uncertainty subject to a production capacity constraint. We show that if firms produce full capacity in the equilibrium, then there are fewer firms in the equilibrium compared to the social optimum even for small levels of yield uncertainty. Furthermore, we prove that if firms do not produce full capacity in the equilibrium, they will not produce full capacity in the social optimum.     

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.     

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.     

Competitive production scheduling: A two-firm,noncooperative finite dynamic game

In this paper, we study the production scheduling problem in a competitive environment. Two firms produce the same product and compete in a market. The demand is random and so is the production capacity of each firm, due to random breakdowns. We consider a finite planning horizon. The scheduling problem is formulated as a finite dynamic game. Algorithms are developed to determine the security, hazard, and Nash policies. Numerical examples are discussed. A single-firm optimization model is also analyzed and it is observed that the production control policy from the single-firm optimization model may not perform well in a competitive environment.     

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.     

Security investment and information sharing in the market of complementary firms: impact of complementarity degree and industry size

We study a differential game of information security investment and information sharing in a market consisting of n complementary firms. Two game approaches, the non-cooperative game and the totally cooperative game, are employed to investigate the steady state strategy of each firm. Under certain conditions, a unique steady state can be obtained for both games. We find that the steady state security investment and information sharing level are not always less in the non-cooperative game than that in the totally cooperative game. In addition, some theoretical analyses are made on the impacts of the complementarity degree and industry size on firms’ steady state strategies for both games. Finally, some numerical experiments are conducted to give some insights related to the instantaneous profit in the steady state. It can be found that a firm will obtain more instantaneous profit in the steady state of the totally cooperative game than that of the non-cooperative game, which emphasizes the importance of coordinating strategies. The effects of the complementarity degree and industry size on the instantaneous profits in the steady state are also obtained through the numerical experiment results.     

Cournot model with investments to change the market size

We present a new deterministic dynamical model on the market size of Cournot competitions, based on Nash equilibria of R&D investment strategies to increase the size of the market of the firms at every period of the game. We compute the unique Nash equilibrium for the second subgame and the profit functions for both firms. Adding uncertainty to the R&D investment strategies, we get a new stochastic dynamical model and we analyse the importance of the uncertainty to reverse the initial advantage of one firm with respect to the other. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

全球化背景下核型创新网络竞争机制研究——基于改进LV-EG模型的仿真分析

在全球化背景下,核型创新网络在向全球创新网络演进的过程中面临多市场竞争和关键资源竞争的双重考验。首先构建全球市场环境下核型创新网络多层次竞合模型;其次,运用Lotka-Volterra模型和演化博弈模型分别剖析核心企业间的竞争关系和尾端企业间的竞合关系,并据此构建改进的LV-EG模型以分析尾端企业竞合关系对核心企业间竞争关系的作用机理;最后,运用matlab对改进的LV-EG模型进行仿真。仿真结果表明:核心企业的尾端企业报酬支付能力、创新产品生产能力、创新环境和网络结构对核型创新网络在全球范围内吸引优质企业并在全球市场环境中获取竞争优势具有重要影响。     

专利中介参与下的技术创新授权策略

考虑外部创新者向两个制造企业及专利中介(PI)拍卖提高质量的创新技术, 获胜者可对创新技术进行授权。基于Stackelberg博弈模型分析两企业的生产决策, 以及PI对市场的影响。研究发现:1)跟随企业在竞价中无法直接赢得专利; 2)若赢得专利, 领导企业只有在渐进式创新中授权给跟随企业, 而PI仅在根本性创新中授权给领导企业; 3)PI的存在会增加外部创新者的利润而降低领导企业的利润。