Bertrand Competition Research Articles

Horizontal outsourcing and price competition: The role of sole sourcing commitment

Previous studies on horizontal outsourcing between competing duopolists emphasize cost factors, such as economies of scale and/or variable cost advantages in Cournot markets, as potential explanations. Our paper studies horizontal outsourcing when two competing firms engage in Bertrand competition, and highlights the important role of sole sourcing commitment. We adopt the framework of a multistage duopoly game that comprises of an incumbent and an entrant. The incumbent has the capability to make a key component in‐house, and the entrant, who is a rival of the incumbent in the downstream market, can source the component from either the incumbent or a supplier not participating in the end‐product market. We find that if the entrant commits to sole sourcing, horizontal outsourcing can occur when the incumbent has a component cost advantage or even a small cost disadvantage over the alternative supplier. Specifically, if the component cost gap is small, horizontal outsourcing may soften downstream market competition and benefit both firms at the expense of inducing higher prices for the consumers. If the incumbent has a significant cost advantage, horizontal outsourcing may lead to an increased downstream price war by expanding the total supply of end products. Without sole sourcing commitment, horizontal outsourcing occurs only when the incumbent has a cost advantage, and it always strengthens downstream price competition. By contrast, if the firms engage in downstream Cournot competition, sole sourcing commitment has no impact on the adoption of horizontal outsourcing, and the entrant sources from her rival only when the incumbent enjoys a significant cost advantage. Finally, we also study various extensions to check and confirm the robustness of our main results to key model assumptions.

Endogenous spillovers in a non‐tournament R&D duopoly under uncertainty

Including R&D risk, this paper considers the choices of R&D spillovers in a simple non‐tournament cost‐reducing R&D duopoly game with Bertrand competition. It turns out that the two firms never disclose any of their R&D information when considering their R&D non‐cooperatively. However, if the firms decide their R&D cooperatively, we show, though they would always fully share their information when the risk of R&D is low, they would not disclose any of their R&D information when the market competition is fierce, the R&D risk is high and the R&D is efficient.

A Note on Input Price Discrimination Under Bertrand Competition: Simultaneous vs. Sequential Contracting

A Note on Input Price Discrimination Under Bertrand Competition: Simultaneous vs. Sequential Contracting

Online Assortment and Market Segmentation under Bertrand Competition with Set-Dependent Revenues

We consider an online assortment problem with $[n]:=\{1,2,\ldots,n\}$ sellers, each holding exactly one item $i\in[n]$ with initial inventory $c_i\in \mathbb{Z}_+$, and a sequence of homogeneous buyers arriving over a finite time horizon $t=1,2,\ldots,m$. There is an online platform whose goal is to offer a subset $S_t\subseteq [n]$ of sellers to the arriving buyer at time $t$ to maximize the expected revenue derived over the entire horizon while respecting the inventory constraints. Given an assortment $S_t$ at time $t$, it is assumed that the buyer will select an item from $S_t$ based on the well-known multinomial logit model, a well-justified choice model from the economic literature. In this model, the revenue obtained from selling an item $i$ at a given time $t$ critically depends on the assortment $S_t$ offered at that time and is given by the Nash equilibrium of a Bertrand game among the sellers in $S_t$. This imposes a strong dependence/externality among the offered assortments, sellers' revenues, and inventory levels. Despite that challenge, we devise a constant competitive algorithm for the online assortment problem with homogeneous buyers. We also show that the online assortment problem with heterogeneous buyers does not admit a constant competitive algorithm. To compensate for that issue, we then consider the assortment problem under an offline setting with heterogeneous buyers. Under a mild market consistency assumption, we show that the generalized Bertrand game admits a pure Nash equilibrium over general buyer-seller bipartite graphs. Finally, we develop an $O(\ln m)$-approximation algorithm for optimal market segmentation of the generalized Bertrand game which allows the platform to derive higher revenues by partitioning the market into smaller pools.

Vertical cross‐ownership, input price discrimination, and social welfare

AbstractIn this paper, we analyze the impact of vertical cross‐ownership with input price discrimination on social welfare. A higher degree of product differentiation will raise industry profit, consumer surplus, and social welfare; under forward cross‐ownership, a higher degree of cross‐ownership has the same effect, in addition, it will reduce rival firm's profit and increase upstream firm's profit; however, under backward cross‐ownership, a higher degree of cross‐ownership has an opposite effect. Furthermore, under Cournot and Bertrand competition, forward cross‐ownership will incentivize downstream firms to produce more via a lower input price, achieving the above effect.

Agency encroachment and information sharing: cooperation and competition in freight forwarding market

ABSTRACT The information exchange between the forwarder and vessel operating common carrier (VOCC) directly leads to a shortage or surplus of capacity and influences operational efficiency. Meanwhile, the development of information technology has inspired VOCCs to establish online booking platforms, which has changed the traditional booking behavior of shippers. Thus, this paper investigates the equilibriums of platform encroachment and information sharing with two symmetric VOCCs and a forwarder. Using a game-theoretic model, it can be characterized as Stackelberg-Nash game with Bertrand competition to determine whether to encroach existing freight forwarding market and share information or not. We observe whether freight forwarder shared information is affected by the encroachment strategy of VOCCs and the market demand state. Further, the encroachment strategy can prompt freight forwarder to share information with VOCCs if the magnitude of high demand is lower. In addition, for VOCCs, the best chance of establishing online platforms is when the magnitude of high demand is relatively low, not when the demand state has increased.

Agency or Wholesale? The Role of Retail Pass-Through

With the rapid growth of e-commerce, agency selling is currently gaining popularity among online retailers (e-tailers). Prior research implicitly abstracts away cross-brand pass-through under traditional wholesale selling (i.e., how the retail price of another brand adjusts to changes in a given brand’s wholesale price) and suggests that a shift to agency selling benefits e-tailers but harms suppliers. As an important counterweight to this result, we discover that an e-tailer’s choice regarding selling format is critically moderated by retail pass-through behavior. On the one hand, agency selling can improve channel efficiency compared with wholesale selling. On the other hand, the relative intensity of supplier competition between these two selling formats is ambiguous. We show that the existing result applies only for a nonnegative cross-brand pass-through rate (e.g., under linear demands); otherwise (e.g., under multiplicative or exponential demands), the opposite may hold. Interestingly, we find that the conflict over the preference of selling format may not arise, and that all channel members could be better off with wholesale selling. Compared with the case of Bertrand competition, the e-tailer is even more likely to adopt wholesale selling under Cournot competition. Finally, under agency selling with an endogenous commission fee, we advise caution regarding the seemingly innocuous normalization of suppliers’ marginal costs. Surprisingly, suppliers may benefit from higher marginal costs. Overall, our findings not only shed light on the theory of agency selling but also provide a plausible explanation for the observation that wholesale selling continues to prevail in online markets. This paper was accepted by Eric Anderson, marketing.

Retailer's selling mode choice under different competition forms

AbstractWe examine the online retailer's selling mode choice under different competition forms in an online retailing supply chain. Four models based on two selling modes (i.e., agency selling and direct selling) and two competition forms (i.e., Bertrand and Cournot) are constructed, and the conditions for the online retailer to choose the optimal selling mode are identified. The results show that the online retailer's optimal choice of selling mode is mainly affected by the direct selling cost under Bertrand competition, whereas it is affected jointly by the direct selling cost, competition intensity, and commission rate under Cournot competition. Additionally, in the direct selling mode, both the online retailer and platform can obtain more profits under Cournot competition; however, in the agency selling mode, the online retailer can benefit from Bertrand competition when the commission rate is moderate, and Cournot competition otherwise. Finally, the effects of competition intensity, commission rate, and direct selling cost on the profits of the online retailer and platform are investigated by numerical analysis.

Non‐cooperative and cooperative environmental corporate social responsibility with emission taxes

This study examines emission taxes and environmental corporate social responsibility (ECSR) under cooperative and non‐cooperative regimes, respectively, and compares Cournot and Bertrand competitions. We show that (i) there exists substitutability between emission taxes and ECSR, while the cooperative case always yields lower emission taxes and higher ECSR; (ii) environmental damage and social welfare are independent of types of ECSR under Cournot, but both are higher in the cooperative ECSR under Bertrand; and (iii) the cooperative ECSR cannot achieve socially desirable outcomes, whereas the non‐cooperative ECSR is beneficial to society under low marginal damage.

Weight assigned to a rival's profit by an advantaged firm in relative performance evaluation with Cournot–Bertrand competition

This study examines the weight placed on a rival's profit under asymmetric cost and Cournot–Bertrand competition. From our model analysis, when an advantaged firm decides quantity and a disadvantaged firm decides a price, we find the case where each firm set positive weight placed on a rival's profit. Our result suggests that decision variables in a product market are important to consider CEOs' implicit compensation contract in empirical research. In addition, it is interesting to demonstrate the advantaged firm sets positive weight placed on a rival's profit under quantity decision.

On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game

A discreet fractional-order Cournot–Bertrand competition duopoly game is introduced based on the fractional-order difference calculus of the Caputo operator. The model is designed when players can make long memory decisions. The local stability of equilibrium points is discussed for the proposed model. Some numerical simulations explore the model’s bifurcation and chaos by employing bifurcation diagrams, phase portraits, maximal Lyapunov exponents, and time series. According to our findings, the fractional-order parameter has an effect on the game’s stability and dynamics.

Cournot–Bertrand comparisons under R&D competition: Output versus R&D subsidies

AbstractWe compare Cournot and Bertrand competitions with R&D investment under output versus R&D subsidy policies. We demonstrate that Cournot firms invest more (less) in R&D and the government grants more (less) subsidies than for Bertrand firms with output (R&D) subsidies. We also find that both competition modes yield the same welfare with output subsidy, while Bertrand yields higher welfare than Cournot with R&D subsidy. Finally, firms' profits and welfare in Cournot are higher under output subsidies, while they can be higher in Bertrand under R&D subsidies if the product substitutability is high and the firm's R&D investment is efficient.

Emission tax and strategic environmental corporate social responsibility in a Cournot–Bertrand comparison

This study considers the strategic relations between emission tax and environmental corporate social responsibility (ECSR) in a Cournot–Bertrand comparison and analyzes two different timings of the games between a tax-then-ECSR (T game) and an ECSR-then-tax (E game). We show that the T game always yields higher emission tax than the E game irrespective of competition modes, but lower ECSR under Cournot competition and higher ECSR when the marginal damage is high under Bertrand competition. We also show that compared with Bertrand competition, Cournot competition yields lower (higher) ECSR in the T (E) game but lower emission tax in the E game and higher emission tax when the product substitutability is low in the T game. We finally show that firms endogenously choose Cournot competition with the commitment of the E game irrespective of marginal damage and product substitutability.

Welfare Consequence of Passive Cross-Ownership: Cournot vs. Bertrand Competition

Welfare Consequence of Passive Cross-Ownership: Cournot vs. Bertrand Competition

The development of the market structure of heterogeneous firms

The article focuses on oligopolistic market which development is modeled with a simulation of firms operating in them. In our model, we take into account findings in theoretical and empirical research of the new trade theory, specifically – the heterogeneity of firms in terms of their productivity and product quality. In the model, firms are allowed to evaluate over the years taking yearly decisions regarding investment into the improvement of product quality and productivity. As a result of this modelling, the authors suggest that in the conditions of imperfect Bertrand competition, firms are not only affected by other firms and market structures in the market, but the firms themselves can act to their advantage changing the competitive environment and subsequently – market structure. Also, the model shows that firms with higher productivity and lower marginal costs do not pass on all the benefits of such savings to their buyers - they apply higher margins and earn higher profits. However, firms that end up winning over the market in the simulation model, lose incentives for further investment, especially in marginal cost-cutting innovations.

Product differentiation and populistic entry strategies in a mortgage market with Bertrand competition

PurposeThe purpose of this paper is to analyse the interaction between a profit maximising mortgagor and a newcomer to a mortgage market with Bertrand competition where the newcomer has a populistic entry strategy and undercuts mortgage market rates. The intention of the paper is to relate the populistic entry strategy to mortgage market characteristics and the strategic market position of both the established mortgagor and the newcomer in question.Design/methodology/approachThe paper analyses a mortgage market by combining the behaviour of a profit maximising mortgagor with that of a newcomer to the mortgage market which has a populistic entry strategy and does not maximise profits. The short-run market solution provides comparative statics on the strategic market position of both the established mortgagor and the newcomer to the mortgage market during the entry phase both related to product differentiation and to price mirroring and undercutting of mortgage rates.FindingsThe model finds a mortgage market solution where a lower mortgage rate helps the newcomer gain a customer base. As the newcomer's strategy to mirror prices makes it unable to pass-through funding cost to its mortgage rate, the strategy is unsustainable over time. The established mortgagor has a strategically beneficial position as the mortgage market rates only relate to its funding cost. Unless the newcomer has a funding cost advantage, the established mortgagor has a higher interest rate margin. Differentiation impacts the newcomers’ interest rate margin positively. If the newcomer lacks a funding cost advantage, there is a critical mirroring rate that ensures it a higher interest rate margin. The higher the newcomers’ own funding cost, the higher is the upper bound for price mirroring, relating market entry to a small undercutting of mortgage rates and a mortgage market with weak competition. The funding cost of the established mortgagor pulls pricing in the opposite direction, allowing for a lower mirroring rate and tougher mortgage market competition during entry.Originality/valueThe paper aims to contribute to the understanding of market equilibrium in the absence of profit maximising behaviour. Framing a mortgage market in terms of a duopoly where a newcomer enters with a populistic entry strategy offering a lower mortgage rate and a mortgage product with a different loan-to-value (LTV) ratio, a novel mortgage market case comes about. The populistic entry strategy produces an augmented reaction curve, crucial for the mortgage market rates.

Bertrand competition under asymmetric conditions

Abstract Analyzing price competition through game theory is one of the most important frameworks of oligopoly theory, especially in industrial organizations. Numerous studies have been conducted in this direction, as companies are forced to adjust their sustainable pricing policy to operate in the long term. Thus, the players make a regular adjustment of the pricing strategy. Of all the models developed based on Bertrand’s reference model (1883), the most analyzed were those in which informational symmetry predominated. Since informational symmetry presents only a theoretical framework, economists have turned their attention to information asymmetry. This type of information best describes a complex economic game, as it creates an information gap between players and generates opportunities in the decision-making process. Thus, asymmetric information is the main parameter of the decision-making process that determines decision makers to resort to different decision strategies than those assumed by the analytical model. Any asymmetric Bertrand model predicts competitive and efficient market outcomes, a direct relationship between a firm’s conduct, market structure and finally market performance. This paper undertakes an analysis of the Bertrand model in the case of demand and asymmetric costs. We determine the Bertrand-Nash equilibrium under the scenario in which close, but not perfect substitutes exist for the differentiated product with hypothetical data. Then we highlight what happens with profits when we consider that discrete cross marginal demand gradually increases. For more research, there are numerous studies based on sequential games, Bayesian games and signaling games both in discrete time and in continuous time.

Endogenous Expectations Management with Network Effects: A Note

Abstract We examine the endogenous choice of commitment device to consumers’ expectations with network effects. Under Cournot competition, we show that choosing commitment to expectations for each firm is a dominant strategy regardless of the strength of network effects. However, under Bertrand competition, three types of commitment with both/no commitment/multiple emerge in equilibrium depending on the strength of network effects. Thus, we obtain different Pareto efficiency between Bertrand and Cournot competition, depending on the intensity of competition.

Implications of Price Matching in Supply Chain Negotiation

Problem definition: Few papers have explored the impact of price matching negotiation (PM), in which a channel matches its price with the resulting wholesale price bargained by another channel, on firms’ performances, consumer welfare, and social welfare, with and without supply chain coordination. Academic/practical relevance: Negotiation has been widely seen in determining both uniform and discriminatory wholesale prices, which affect outcomes of competitive supply chain practices. Methodology: To characterize the PM mechanism, we use game theory and Nash bargaining theory to compare PM with simultaneous negotiation (SN) through a common-seller two-buyer differentiated Bertrand competition model. Results: Our analysis reveals that PM can benefit the seller but hurt all buyers, which is at odds with some fair wholesale pricing clauses intending to protect buyers. Under coordination with side payments, however, all firms can conditionally benefit more from PM than from SN. Despite firms’ gains, PM leads to less consumer utility and social welfare compared with SN, unless the second buyer in PM is considerably less powerful than the first buyer. Coordination further worsens PM’s negative impact on consumer utility and social welfare. Moreover, the existence of a spot market can increase the wholesale price in PM, hurting buyers, consumers, and society. Furthermore, the qualitative results about PM remain robust under an alternative disagreement point for PM, multiple buyers, and other extensions. Managerial implications: This paper delivers insights on when price matching in supply chain wholesale price negotiation can benefit a seller, buyers, consumers, and society in a variety of scenarios. It advocates how managers can use PM to their own advantages and provides rationale to decision makers for policy regulations regarding wholesale pricing.

Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game

This paper considers a Bertrand competition between two firms whose decision variables are derived from a quadratic utility function. The first firm produces new products with their own prices while the second firm re-manufactures returned products and sells them in the market at prices that may be less than or equal to the price of the first firm. Dynamically, this competition is constructed on which boundedly rational firms apply a gradient adjustment mechanism to update their prices in each period. According to this mechanism and the nature of the competition, a two-dimensional piecewise smooth discrete dynamic map was constructed in order to study the complex dynamic characteristics of the game. The phase plane of the map was divided into two different regions, separated by border curve. The equilibrium points of the map, in each region on where they are defined, were calculated, and their stability conditions were investigated. Furthermore, we conducted a global analysis to investigate the complex structure of the map, such as closed invariant curves, periodic cycles, and chaotic attractors and their basins, which cause qualitative changes as some parameters are allowed to vary.