Bertrand Model Research Articles

Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions

In analyses of sponsored search auctions for online advertising, it is customary to model the dynamic game of incomplete information by considering a static game of complete infor mation. This approach is used in Benjamin Edelman, Michael Ostrovsky and Michael Schwarz (2007) (EOS), Hal R. Varian (2007), and the subsequent literature. Modeling complex interactions in uncertain environments as games of complete information has a long history. For example, the Bertrand model of oligopolistic competition posits that companies know their competitors' costs based on their experience from prior interactions. The use of a static game of complete infor mation often offers important benefits. For one, it is tractable?avoiding complex multi period information sets in a dynamic game. Furthermore, a suitably chosen static game can capture important characteristics of the under lying dynamic game. When a game is repeated over an extended period, there is good reason to think participants will learn many characteris tics of their counterparts?supporting the use of a complete information model. Yet the use of a static game of complete information is also unsatisfying. There is no clear way to identify which (if any) equilibria of the static game of complete information are a relevant approximation of the equilibria of the dynamic game of incomplete information.

The Inefficiency of Market Transparency – A Model with Endogenous Entry

Including the entry decision in a Bertrand model with imperfectly informed consumers, we introduce a trade-off at the level of social welfare. On the one hand, market transparency is beneficial when the number of firms is exogenously given. On the other, a higher degree of market transparency implies lower profits and hence makes it less attractive to enter the market in the first place. It turns out that the second effect dominates: too much market transparency has a detrimental effect on consumer surplus and on social welfare.

Equilibrium vertical differentiation in a Bertrand model with capacity precommitment

Both quality differentiation and capacity commitment have been shown to relax price competition. However, their joint influence on the outcome of price competition has not yet been assessed. In this article, we consider a three-stage game in which firms choose quality, then commit to capacity and, finally, compete in price. When the cost of quality is negligible, we show that firms do not differentiate their products in a subgame perfect equilibrium, in other words, capacity precommitment completely eliminates the incentive to differentiate by quality.

Equilibrium Vertical Differentiation in a Bertrand Model with Capacity Precommitment

Both quality differentiation and capacity commitment have been shown to relax price competition. However, their joint influence on the outcome of price competition has not yet been assessed. In this article, we consider a three stage game in which firms choose quality, then commit to capacity and, finally, compete in price. When the cost of quality is negligible, we show that firms do not differentiate their products in a subgame perfect equilibrium, in other words, capacity precommitment completely eliminates the incentive to differentiate by quality.

Endogenous Timing and Banking Competition in a Mixed Oligopoly: A Theoretical Perspective on the Banking Industry in China

Based on the background of the banking industry in China, this paper establishes Cournot, Bertrand and Stackelberg mixed oligopoly competition models with deposit and interest rates as strategic variables between a representative state-owned bank and a representative foreign bank. We discuss and compare the equilibrium deposits, interest rates and profits in different market structures. More importantly, considering the endogenous timing setup and taking the extended game with observable delay as the basic model, we analyze the competition results of the mixed duopoly at different market structures and make numerical simulations in order to get the outcomes of the extended game. It is found that, in the deposit competition with endogenous timing, if two banks have the same deposit return rate, the simultaneous move could become the final result; If the deposit return of the foreign bank is more than twice that of the state-owned bank, all SPNEs of the extended game are sequential, i.e one bank will lead, the other will follow. If the state-owned bank’s profit in Cournot is larger than that of the state-owned bank as the Stackelberg follower, the only SPNE will be (E, L), i.e. the state-owned bank will lead and the foreign bank will follow. Additionally, in the interest rate competition with endogenous timing, if the degree of nationalization is no larger than 75% as well as two banks have the same deposit return rate, the final SPNEs of the extended game are sequential and the simultaneous move can not become the SPNE.

The study of dynamic process of the triopoly games in chinese 3G telecommunication market

At first, the paper described a brief history of communication in China. In 2008, the third generation (3G) telecommunication technologies began to develop. In Chinese 3G telecommunication market, there are three oligopolistic competitors. In order to study competing process of the triopoly, the paper considered a Bertrand model with bounded rational. A triopoly game is modeled by three nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system were obtained. Numerical simulations were used to show bifurcations diagrams, the maximum Lyapunov exponent and sensitive dependence on initial conditions. We observed that increasing the speed of adjustment of bounded rational player might change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. Thus, it will be difficult to make strategy and to forecast for each enterprise. It might cause the telecom markets to be irregular. The analysis and results in this paper are important for Chinese telecommunication markets, the same to mathematics.

Research on Bertrand Dual-Oligopoly Dynamic Game Model

In this article, we study the equilibrium solution and the dynamic change process of the Bertrand price competition model under the condition of dual-manufactures, give the model of dynamic change, prove that whatever manufactures choose about price, the equilibrium solution only exists, and prove that the manufacture’s price change process must be the monotonic process, and develop relative conclusions of the Bertrand model.

Maximum-revenue tariff under Bertrand duopoly with unknown costs

This paper considers an international trade under Bertrand model with differentiated products and with unknown production costs. The home government imposes a specific import tariff per unit of imports from the foreign firm. We prove that this tariff is decreasing in the expected production costs of the foreign firm and increasing in the production costs of the home firm. Furthermore, it is increasing in the degree of product substitutability. We also show that an increase in the tariff results in both firms increasing their prices, an increase in both expected sales and expected profits for the home firm, and a decrease in both expected sales and expected profits for the foreign firm.

Reciprocal Dumping With Product Differentiation

This paper examines if international trade can reduce total welfare in an international oligopoly with differentiated goods. We show that intra-industry trade, i.e. reciprocal dumping, can result in lower total surplus than autarky in a Cournot model for any degree of product differentiation. Moreover, trade can reduce welfare compared to autarky in a Bertrand model when the local markets are sufficiently competitive and products are sufficiently close substitutes. Otherwise it unambiguously increases welfare.

Reciprocal Dumping with Product Differentiation*

AbstractThis paper examines if international trade can reduce total welfare in an international oligopoly with differentiated goods. We show that intra‐industry trade, i.e. “reciprocal dumping,” can result in lower total surplus than autarky in a Cournot model for any degree of product differentiation. Moreover, trade can reduce welfare compared to autarky in a Bertrand model when the local markets are sufficiently competitive and products are sufficiently close substitutes. Otherwise it unambiguously increases welfare.

APPLICATION OF GAME THEORY FOR DUOPOLY MARKET ANALYSIS

The paper provides the analysis of game theory models application to identify duopoly market equilibrium (quantities sold and market prices), to evaluate and compare the results of enterprises in a market. The purpose of the analysis is to determine to what extent theoretical models correspond to real life, that is how reliable they are in supporting and estimating decisions of duopoly companies, fortifying market prices and quantities sold, evaluating company's competing positions and possibilities for decision co‐ordination. To describe discrete strategies equilibrium the “Prisoner's Dilemma” model is applied to a hypothetic market entrance game with possible side payments. Further analysis of the market entrance game incorporates mixed strategies based “Matching Pennies” model in case discrete strategies equilibrium does not exist. Continuous strategies are described analyzing hypothetic duopoly by applying Cournot, Stackelberg and Bertrand models. The first and the second mover advantage issues are raised comparing outcomes of dynamic Stackelberg and Bertrand games for a leader and a follower. Stability and utility of cartel agreement for its participants is mathematically supported with the help of a multi‐step repeated Cournot game. Having described, compared and applied the main game theory models to artificial duopoly market situations, the author passes over to the comparative analysis of the models’ weaknesses and problems related to their practical application.

The dynamics of Bertrand model with bounded rationality

The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.

Competition Between Firms that Bundle Information Goods

Information goods are characterized by high fixed (first-copy) costs, but very low costs for the production of additional copies. Marginal costs of electronically-delivered information goods have been further reduced by the remarkable recent decline in computing and digital communication costs. Most previous research focuses on how a monopolist would perform (and the proper regulation to impose) in such an environment. Achieving dynamic efficiency is difficult because pricing at marginal cost (which is statically efficient) eliminates the incentive to invest in the creation of new content. Recently, the strategy of bundling numerous goods together has been explored in greater detail. Bundling may achieve static efficiency since individuals will face a zero cost on the margin for each item consumed. Yet, dynamic efficiency can be maintained because the producer is able to recover investment costs through bundle sales. This paper analyzes the profitability and welfare properties of bundling in a multi-firm setting. This allows us to explore how incumbents and entrants interact when each firm is selling numerous competing products. Our fundamental conclusion is that even adding only a single firm to this industry with substantial fixed costs and negligible marginal costs will result in much lower prices for consumers, much higher social welfare, and only a moderate reduction in firms' profits regardless of the pricing schemes employed. This outcome is somewhat surprising given that in a standard static two-good Bertrand model, a duopoly would lead to a price war which eliminates the incentive to invest in new content (or to enter the industry in the first place). Although the firms are producing a priori identical items, consumers know that their valuations for the particular items will vary ex post. Thus, no price reduction by one firm can completely eliminate the demand faced by other firms. Although there remains an incentive to invest in new product creation, this incentive is lower than a monopolist would have. As a result, in a dynamic version of this model, the welfare superiority of the duopoly becomes dampened (but not eliminated). Finally, when firms are allowed to sell items both as a bundle and individually, we find that most revenue will be obtained from bundle sales. These results indicate that bundling will persist in a multi-firm setting and suggest that only firms of substantial size will be able to survive in such a market.

Cournot and Bertrand in shipping models with circular markets

Abstract. We investigate two shipping (delivered pricing) duopoly models with circular markets, Cournot and Bertrand. In the Cournot model, maximal distance between two firms becomes the unique equilibrium outcome if transport cost is increasing with distance, irrespective of whether the transport cost function is convex or concave. This result is robust in the sense that cost heterogeneity between two firms does not change the result. In contrast to the Cournot model, this location pattern can fail to be an equilibrium in the Bertrand model.

A Bertrand model of pricing of complementary goods under information asymmetry

Parties in a supply chain, being independent firms, have private information about various aspects of the business not normally available to other parties. We consider a market where customers need to buy two complementary goods as mixed bundle, offered by two separate firms. The demand for each firm is dependent on the pricing strategy of both firms, which, in turn, depends on the quantities offered as per their own forecasts. We present a profit maximization model to obtain optimal strategies for a firm making decisions under information asymmetry. The model follows a simultaneously played Bertrand type game. We contrast and compare three scenarios: (1) when forecast information is asymmetric between the firms; (2) when forecast information is shared between the firms; and (3) when the firms form a strategic alliance.

Small scale entry versus acquisitions of small firms: Is concentration self-reinforcing?

We consider a reduced form model with acquisitions and entry. There are two investors and several small non-investing firms. One investor can acquire a small firm, the other investor decides about market entry. After that all firms play an oligopoly game. We derive conditions under which increasing market concentration arises with myopic firms. We apply the framework to a Cournot model with cost synergies and a Bertrand model where acquisitions extend the product spectrum of a firm.

Strategic pricing in a differentiated product oligopoly model: fluid milk in Boston

AbstractIn an imperfectly competitive industry, differentiated products compete with each other with price rather than quantity as the strategic variable. Several previous studies have employed a generalized Nash–Bertrand model: Liang (1989), Cotterill (1994), Cotterill et al. (2000), and Kinoshita et al. (2002); however, only Liang has explored the theoretical foundations of that model. This article generalizes the Liang two‐good model to three goods. A surprising and important result follows. Price‐conjectural variations do not exist in models with three or more goods. Price‐reaction functions, however, exist in multiple‐good models. We estimate them jointly with a brand‐level demand system to evaluate the total impact of a brand manager's price change on own quantity. In a differentiated product market, this is a useful addition to a partial demand elasticity approach, because a change in one brand's price typically engenders a price reaction by other brands that affects own quantity via substantial cross‐price elasticities among substitutes. Strategic pricing in the Boston fluid milk market was also influenced by the existence of a raw milk price support program, the Northeast Dairy Compact. We find that the advent of the Compact was a focal point event that crystallized a shift away from Nash–Bertrand to more cooperative pricing. If the downstream market is not competitive, one needs to consider strategic price reactions when designing and evaluating agricultural price programs.

An Exposition on the Horizontally Differentiated Products Bertrand Model

Students, in their roles as consumers, are usually more familiar with price competition than with quantity competition. Unfortunately, the Bertrand pricing model is usually given short shrift, relative to the Cournot model, both in the classroom and in textbooks. The richness of the Bertrand model should not be underestimated. We show how the standard textbook parameterization can be used, both analytically and graphically, in determining how variations in product differentiation can affect equilibrium prices and profits. We also show that some of the standard assumptions used in both textbooks and in research are unnecessarily strong. Additionally, we mention the role of advertising and its effects on pricing and profitability as well. The findings are useful in presenting and discussing the Bertrand model in the classroom.

Economic welfare in delivered pricing duopoly: Bertrand and Cournot

We investigate two delivered pricing models. We find that in the Bertrand (Cournot) model the equilibrium distance between two firms' locations is too large (small) for maximum social welfare, while it is too small for maximum consumer surplus in both models.

Technological Improvement and Industrial Employment

This paper looks at how the entry of a multinational in the domestic market of an industry in a developing country affects the total industry wide employment. It is assumed that the technology of the multinational is more efficient than the domestic technology. Standard Cournot oligopoly and Bertrand models are used. When a multinational enters the market of a domestic monopoly employment increases only if technology differences are very small or very large. Entry into markets controlled by domestic oligopolies is associated with an increase in employment only if the difference in domestic and multinational technologies does not exceed a certain magnitude which is inversely related to the existing competition. The results can be generalised to any case in which the entrant into the industry is more efficient than the existing firms.