• Title/Summary/Keyword: Subgame-perfect equilibrium

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A Study on the International R&D Competition and Optimal Tariff (국제 R&D 경쟁과 최적관세)

  • Li, Dong-Sheng;Lee, Jong-Min
    • Korea Trade Review
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    • v.41 no.2
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    • pp.29-60
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    • 2016
  • Research and Development(R&D) investment is an issue of central importance in any economy. In this paper we analyze the relationship between R&D spillovers and trade-related variables, using a two-stage model where duopolists simultaneously decide on R&D in the first stage and engage in Cournot competition in the second stage. We characterized and compared the free-trade and trade-restriction R&D equilibrium in a two-stage game of R&D investment followed by Cournot market competition. We also assessed the impact of varying the R&D spillover on the equilibrium outcomes and tariff. We showed for both free trade and protection cases that there exists a unique symmetric solution(subgame perfect Nash equilibrium). As the solution, while analytical, cannot be stated in closed form, we resorted to numerical experiments to investigate the equilibrium results. Our estimates indicate for both free trade and protection cases that the level of R&D investment and the rate of R&D expenditure decrease as the degree of R&D spillovers increases, and that there is an inverse relation between the degree of R&D spillovers and level of protection. The latter implies that the larger the degree of R&D spillovers, the lesser the level of protection.

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Cooperative Sales Promotion in Manufacturer-Retailer Channel under Unplanned Buying Potential (비계획구매를 고려한 제조업체와 유통업체의 판매촉진 비용 분담)

  • Kim, Hyun Sik
    • Journal of Distribution Research
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    • v.17 no.4
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    • pp.29-53
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    • 2012
  • As so many marketers get to use diverse sales promotion methods, manufacturer and retailer in a channel often use them too. In this context, diverse issues on sales promotion management arise. One of them is the issue of unplanned buying. Consumers' unplanned buying is clearly better off for the retailer but not for manufacturer. This asymmetric influence of unplanned buying should be dealt with prudently because of its possibility of provocation of channel conflict. However, there have been scarce studies on the sales promotion management strategy considering the unplanned buying and its asymmetric effect on retailer and manufacturer. In this paper, we try to find a better way for a manufacturer in a channel to promote performance through the retailer's sales promotion efforts when there is potential of unplanned buying effect. We investigate via game-theoretic modeling what is the optimal cost sharing level between the manufacturer and retailer when there is unplanned buying effect. We investigated following issues about the topic as follows: (1) What structure of cost sharing mechanism should the manufacturer and retailer in a channel choose when unplanned buying effect is strong (or weak)? (2) How much payoff could the manufacturer and retailer in a channel get when unplanned buying effect is strong (or weak)? We focus on the impact of unplanned buying effect on the optimal cost sharing mechanism for sales promotions between a manufacturer and a retailer in a same channel. So we consider two players in the game, a manufacturer and a retailer who are interacting in a same distribution channel. The model is of complete information game type. In the model, the manufacturer is the Stackelberg leader and the retailer is the follower. Variables in the model are as following table. Manufacturer's objective function in the basic game is as follows: ${\Pi}={\Pi}_1+{\Pi}_2$, where, ${\Pi}_1=w_1(1+L-p_1)-{\psi}^2$, ${\Pi}_2=w_2(1-{\epsilon}L-p_2)$. And retailer's is as follows: ${\pi}={\pi}_1+{\pi}_2$, where, ${\pi}_1=(p_1-w_1)(1+L-p_1)-L(L-{\psi})+p_u(b+L-p_u)$, ${\pi}_2=(p_2-w_2)(1-{\epsilon}L-p_2)$. The model is of four stages in two periods. Stages of the game are as follows. (Stage 1) Manufacturer sets wholesale price of the first period($w_1$) and cost sharing level of channel sales promotion(${\Psi}$). (Stage 2) Retailer sets retail price of the focal brand($p_1$), the unplanned buying item($p_u$), and sales promotion level(L). (Stage 3) Manufacturer sets wholesale price of the second period($w_2$). (Stage 4) Retailer sets retail price of the second period($p_2$). Since the model is a kind of dynamic games, we try to find a subgame perfect equilibrium to derive some theoretical and managerial implications. In order to obtain the subgame perfect equilibrium, we use the backward induction method. In using backward induction approach, we solve the problems backward from stage 4 to stage 1. By completely knowing follower's optimal reaction to the leader's potential actions, we can fold the game tree backward. Equilibrium of each variable in the basic game is as following table. We conducted more analysis of additional game about diverse cost level of manufacturer. Manufacturer's objective function in the additional game is same with that of the basic game as follows: ${\Pi}={\Pi}_1+{\Pi}_2$, where, ${\Pi}_1=w_1(1+L-p_1)-{\psi}^2$, ${\Pi}_2=w_2(1-{\epsilon}L-p_2)$. But retailer's objective function is different from that of the basic game as follows: ${\pi}={\pi}_1+{\pi}_2$, where, ${\pi}_1=(p_1-w_1)(1+L-p_1)-L(L-{\psi})+(p_u-c)(b+L-p_u)$, ${\pi}_2=(p_2-w_2)(1-{\epsilon}L-p_2)$. Equilibrium of each variable in this additional game is as following table. Major findings of the current study are as follows: (1) As the unplanned buying effect gets stronger, manufacturer and retailer had better increase the cost for sales promotion. (2) As the unplanned buying effect gets stronger, manufacturer had better decrease the cost sharing portion of total cost for sales promotion. (3) Manufacturer's profit is increasing function of the unplanned buying effect. (4) All results of (1),(2),(3) are alleviated by the increase of retailer's procurement cost to acquire unplanned buying items. The authors discuss the implications of those results for the marketers in manufacturers or retailers. The current study firstly suggests some managerial implications for the manufacturer how to share the sales promotion cost with the retailer in a channel to the high or low level of the consumers' unplanned buying potential.

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Optimal Incentives for Customer Satisfaction in Multi-channel Setting (멀티채널에서의 고객만족제고 인센티브 연구)

  • Kim, Hyun-Sik
    • Journal of Distribution Research
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    • v.15 no.1
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    • pp.25-47
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    • 2010
  • CS is one of the major concerns of managers in the world because it is well known to be a key medium construct for firms' superior outcome. One of the major agents for CS management is retailers. Firms try to manage not only employees but also retailers to promote CS behaviors. And so diverse incentives are used to promote their CS behaviors under diverse channel setting such as multi-channel. However in spite of the rising needs there has been scarce studies on the optimal incentive structure for a manufacturer to offer competing retailers at the multi-channel. In this paper, we try to find better way for a manufacturer to promote the competing retailers' CS behaviors. We investigated how to promote the retailers' CS behavior via game-theoretic modeling. Especially, we focus on the possible incentive, CS bonus type reward introduced in the studies of Hauser, Simester, and Wernerfelt(1994) and Chu and Desai(1995). We build up a multi stage complete information game and derive a subgame perfect equilibrium using backward induction. Stages of the game are as following. (Stage 1) Manufacturer sets wholesale price(w) and CS bonus($\eta$). (Stage 2) Both retailers in competition set CS effort level($e_i$) and retail price($p_i$) simultaneously. (Stage 3) Consumers make purchasing decisions based on the manufacturer's initial reputation and retailers' CS efforts.

    Structure of the Model We investigated four issues about the topic as following: (1) How much total incentive is adequate for a firm of a specific level of reputation to promote retailers' CS behavior under multi-channel setting ?, (2) How much total incentive is adequate under diverse level of complimentary externalities between the retailers' CS efforts to promote retailers' CS behavior?, (3) How much total incentive is adequate under diverse level of cost to make CS efforts to promote retailers' CS behavior?, (4) How much total incentive is adequate under diverse level of competition between retailers to promote retailers' CS behavior? Our findings are as following. (1) The higher reputation has the manufacturer, the higher incentives for retailers at multi-channel are required in the equilibrium.
    shows the increasing pattern of optimal incentive level along the manufacturer's reputation level(a) under some parameter conditions(b=1/2;c=0;$\beta$=1/2). (2) The bigger complimentary externalities exists between the retailers' CS efforts, the higher incentives are required in the equilibrium.
    shows the increasing pattern of optimal incentive level along the complimentary externalities level($\beta$) under some parameter conditions(a=1;b=1/2;c=0). (3) The higher is the retailers' cost, the lower incentives are required in the equilibrium.
    shows the decreasing pattern of optimal incentive level along the cost level(c) under some parameter conditions(a=1;b=1/2;$\beta$=1/2). (4) The more competitive gets those two retailers, the higher incentives for retailers at multi-channel are required in the equilibrium.
    shows the increasing pattern of optimal incentive level along the competition level(b) under some parameter conditions(c=0;a=1;$\beta$=1/2). One of the major contribution points of this study is the fact that this study is the first to investigate the optimal CS incentive system under multi-channel setting.

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The strategic behaviors of incumbent pharmacy groups in the retail market of pharmaceuticals in response to the entry trials by the online platform firms delivering medicines - A perspective of market entry deference model in game theory (온라인 의약품배송플랫폼기업의 시장 진입 시도에 대한 기존 의약품 공급자의 전략적 행동 - 게임이론의 시장진입 저지 모형 관점)

  • Lee, Jaehee
    • The Journal of the Convergence on Culture Technology
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    • v.8 no.4
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    • pp.303-311
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    • 2022
  • Recently the telemedicine platform firms which have been temporarily permitted since COVID-19 outbreak have increasingly provided online prescription drugs delivery, causing concerns among incumbent providers of medicine, some of whom began to take aggressive actions again them. In this study, using game theoretic market entry - deterrence model, we show that although the incumbent medicine provider can effectively deter entry by the telemedicine platform firms by its preemptive action, accommodation could be a optimal action when telemedicine platform firms already have penetrated the market with their being permitted to do business due to the COVID-19. However, for the incumbent to cooperate for the successful change in the retail market for medicines, policies like placing a ceiling on the maximum number of taking prescriptions by the pharmacists a day in the telemedince platform network, providing favorable exposure of community pharmacists on the telemedicine platform user interface, and allowing community pharmacies to participate as shareholders of the telemedicine platform firms in its initial public opening of capital, are suggested.