Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

Economic natural selection in Bertrand and Cournot settings

We study economic natural selection in classical oligopoly settings. When underlying pure strategies consist of a finite number of prices, convex monotonic dynamics always converge under a weak condition to the smallest price in the support of the initial state that exceeds marginal cost. When underlying pure strategies consist of a finite number of quantities, monotonic dynamics always converge under a specific condition to a quantity equal or similar to classical Cournot equilibrium.     

Winner-take-all price competition

Summary. We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes. Received: April 7, 2000; revised version: September 14, 2000     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.     

Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Delegation and polarization of platforms in political competition

Summary. We consider a model of political competition among two ideological parties who are uncertain about the distribution of voters. The distinguishing feature of the model is that parties can delegate electoral decisions to candidates by nomination. It is shown that if the credible platform commitments of the candidates is feasible, then at least one of the parties nominates in equilibrium to a candidate who has an ideology that is more radical than the delegating party's ideology. In a variety of circumstances, this, in turn, yields a polarization of equilibrium policy choices of the candidates. It is thus argued formally here that strategic nomination of the candidates may well be one of the major reasons behind the well documented observation that the platforms associated with the political parties in two-party democracies are often surprisingly polarized. Received: January 10, 2002; revised version: May 8, 2002 RID="*" ID="*" We thank Alberto Alesina, Levent Ko?kesen, Antonio Merlo, Ronny Razin, Vijay Krishna, Alessandro Lizzeri, and seminar participants at Alicante, Columbia, Copenhagen, and NYU for helpful comments. We also thank an anonymous referee for its useful suggestions. A good fraction of this research was conducted while Ok was a visitor in the Department of Economics at University of Alicante; he thanks for the kind hospitality of this institution. We gratefully acknowledge the financial support from the Spanish Ministry of Education through grant CICYT BEC2001-0535 (Faulí-Oller) and BEC2001-0980 (Ortu?o-Ortín). Correspondence to:I. Ortu?o-Ortin     

On strategic complementarity conditions in Bertrand oligopoly

Summary. For Bertrand duopoly with linear costs, we establish via a single (counter-)example that: (i) A new monotone transformation of the firms' profit functions may lead to the supermodularity of transformed profits when the standard log and identity transformations both fail to do so, and (ii) Topkis's notion of critical sufficient condition for monotonicity of a Bertrand firm's best-reply correspondence cannot be extended to rely only on positive unit costs. Received: January 16, 2001; revised version: March 20, 2002 RID="*" ID="*" This work was completed while the first author was visiting the Institute for Industrial Economics at the University of Copenhagen during Spring 2000. Their financial support and stimulating research environment are gratefully acknowledged. The views expressed here are those of the authors and should not be attributed to the European Commission. Correspondence to: R. Amir     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

The option of joint purchase in vertically differentiated markets

Summary. Within the framework proposed by Mussa and Rosen (1978) for modelling quality differentiation, consumers are assumed to make mutually exclusive purchases. A unique pure strategy equilibrium exists in this case. In this note, we allow consumers to buy simultaneously different variants of the differentiated good. We call this the “joint purchase option”. The paper proposes a detailed analysis of price competition when this option is opened: first, we show that either uniqueness, or multiplicity, or absence of price equilibrium arise, depending on the utility derived from joint purchase relative to exclusive purchase. Second, we characterize these equilibria, whenever they exist. Received: July 25, 2001; revised version: October 21, 2002 RID="*" ID="*" The second author gratefully acknowledges the financial support from Interuniversity Attraction Pole Program- Belgian State- Federal Office for Scientific, Technical and Cultural Affairs under contract PAI 5/26. Correspondence to: X.Y. Wauthy     

Price competition and the Bertrand model: the paradox of the German mobile discount market

We investigate the degree of price competition among telecommunication firms. Underlying a Bertrand model of price competition, we empirically model pricing behaviour in an oligopoly. We analyse panel data of individual pricing information of mobile phone contracts offered between 2011 and 2017. We provide empirical evidence that price differences as well as reputational effects serve as a signal to buyers and significantly affect market demand. Additionally, we find that brands lead to an increase in demand and thus are able to generate spillover effects even after price increase.     

Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001     

Speculative trade, asset prices and investment levels

Summary. In this paper I consider a dynamically complete market model without intrinsic uncertainty. Agents' beliefs are different, but correct in the limit. Some agents are more patient than others. I show that infinitely often share prices are low and the economy stagnates. Also, infinitely often share prices are high and the economy grows. The changes from growth to stagnation and from stagnation to growth are not caused by exogenous shocks. They are caused by speculative trade among agents with different propensities to save and invest. Received: January 8, 2001; revised version: April 11, 2002 RID="*" ID="*" I thank an anonymous referee for helpful comments. I gratefully acknowledge financial support from the National Science Foundation.     

The analytics of search with posted prices

Summary. This paper investigates the characteristics of the optimal posted price in the standard sequential search paradigm. Much of the intuition gleaned from the extensive sequential search literature in which the seller adopts a reservation price does not carry over to the posted price setting. For example, an increase in buyer valuations can lead to a reduction in the optimal posted price. We do, however, provide sufficient conditions on the hazard rate function h which ensure that an increase in demand induces an increase in the optimal posted price. As exhibited herein, the analysis of the posted price model depends critically upon analytical properties of h. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium. Received: October 21, 1999; revised version: March 7, 2000     

Rationalizability and equilibrium in N-person sequential bargaining

Summary. This paper deals with N-person sequential bargaining games with complete information. For N-person sequential bargaining games, uniqueness of the SPE has been obtained by allowing the players to exit with partial agreements. Adopting a non-equilibrium approach, we show that N-person sequential bargaining games with exit are solvable by a refinement of rationalizability for multi-stage games (trembling-hand rationalizability) whatever the impatience of the players. That is, once we adopt the non-equilibrium approach, the exit opportunity still fulfils its original aim: we achieve a unique solution by introducing the exit opportunity. Moreover, this unique solution is the unique SPE. Received: October 30, 1996; revised version: July 7, 1998     

Foreign market entry,upstream market power,and endogenous mode of downstream competition

In a differentiated duopoly model of trade and FDI featuring both horizontal and vertical product differentiation, we examine whether globalization and trade policy measures can generate welfare gains by leading firms to change their mode of competition. We show that when a high-quality foreign variety is manufactured under large frictions due to upstream monopoly power, a foreign firm can become a Bertrand competitor against a Cournot local rival in equilibrium, especially when the relative product quality of the foreign variety is sufficiently high and trade costs are sufficiently low (implying higher input price distortions due to double marginalization). Our results suggest that such strategic asymmetry is welfare improving and that the availability of FDI as an alternative to trade can make welfare-enhancing strategic asymmetry even more likely, especially when both input trade costs and fixed investment costs are sufficiently low and trade costs in final goods are sufficiently large.     

On competition and endogenous firm efficiency

Summary. Conventional wisdom holds that product market competition disciplines firms into efficiency of operation. However, in a well known paper, Martin (1993) has shown that in a linear Cournot setting (with costs determined first and product market competition taking place in a second stage) the exact opposite obtains – a larger number of firms competing in the market implies lower firm efficiency. The note clarifies further the links between market structure and efficiency. Specifically, it argues why (and how) the result derived by Martin (1993) depends upon the assumptions made regarding the structure of demand and nature of conjectures held by firms as to their rivals' behavior. An illustrative counter-example (with Bertrand behavior and non-linear demand) in which entry increases efficiency is provided as well. Received: March 2, 2000; revised version: September 19, 2000     

Product diffusion and pricing with market frictions

Summary. We study pricing and product diffusion in a dynamic general equilibrium framework with product market frictions. Ongoing R&D activity leads, with an endogenously determined probability, to continual improvements in product quality. We characterize the steady-state equilibrium with endogenous product diffusion in which a number of different goods co-exist on the quality ladder. We show that the severity of the economy's market frictions is a crucial determinant of the pricing structure, the product diffusion pattern, the level of R&D investment, the rate of endogenous growth, the length of Schumpeterian product cycles and the possibility of multiple growth paths. Eliminating market frictions leads to a degenerate product ladder of precisely one step, containing only the most recent product, as in the monopolistic competition literature. Received: August 16, 1999; revised version: March 6, 2001     

Non-cooperative games with a continuum of players whose payoffs depend on summary statistics

Summary. We consider static non-cooperative games with a continuum of small players whose payoffs depend on their own actions and finitely many summary statistics of the aggregate strategy profile. We prove the existence of an equilibrium in pure strategies without any convexity restrictions on payoffs or the common action space. We show that this result applies to a broad class of monopolistic competition models. Received: April 13, 2001; revised version: December 18, 2001 RID="*" ID="*" The result in this paper generalizes a result in my PhD dissertation supervised by M. Ali Khan and Joe Harrington. I thank them for support and encouragement. I also thank Sung Kim, Bruce Nanney, Ashvin Rajan, Kali Rath, and an anonymous referee for comments. The usual disclaimer applies.