A note on undominated Bertrand equilibria

This note shows that the conventional outcome associated with Bertrand competition with homogenous products and different marginal costs is obtained in every Nash equilibrium in which firms use undominated strategies. This strengthens an existence result due to Blume (2003).     

A note on evolutionary stability of Bertrand equilibrium

It is shown that the equilibrium notion of an evolutionary stable strategy (ESS) does have predictive power for standard models of Bertrand competition. This is in contrast to a recent claim by Qin and Stuart (1997). The claim is based on the observation that the solution concept ESS behaves discontinuously when finite (discrete) action games approach an infinite (continuous) action game in the limit. Furthermore, it is argued that from a model-theoretic point of view evolutionary stability in prices (i.e. in the Bertrand model) is quite different from evolutionary stability in quantities (i.e. in the Cournot model).     

A note on merger in mixed duopoly: Bertrand versus Cournot

In this note we analyze the incentives to merge in a mixed duopoly if firms compete in prices or quantities. Our model framework mainly follows Barcena-Ruiz and Garzon (J Econ 80:27–42, 2003) who set up the model with quantity competition. We extend their analysis by analyzing the case of competition in prices. Further we compare the incentives to merge with Bertrand and Cournot competition. Comparing quantity with price competition we can show that a merger is more likely with Cournot competition than with Bertrand competition.     

Observable versus unobservable R&D investments in duopolies

Journal of Economics - We study a quantity-setting duopoly with homogeneous products in which two firms first make their cost-reducing R&D investments, and then compete in quantities. When...     

Optimality and renegotiation in dynamic contracting

We characterize the optimal renegotiation-proof contract in a dynamic principal–agent model in which the type of the agent may change stochastically over time. We show that, under general conditions, the optimal contract with commitment is renegotiation proof even when type realizations are serially correlated. When the renegotiation-proofness constraint is binding, it is always optimal to partially screen the types by offering a menu of choices to the agent; and the distortion induced by the renegotiation-proofness constraint is non-decreasing in the persistence of types.     

A Note on Optimal Industrial Policy Towards Bertrand Homogeneous Duopoly

Recent studies in strategic trade and industrial policy analysis suggest that an investment subsidy, in the form of an R&D subsidy, a capacity subsidy or an advertising subsidy, would be a robust industrial policy recommendation towards an international differentiated oligopoly. However, in this paper, we show that this result does not carry over to the case of a Bertrand homogeneous duopoly. This result together with the fact that the optimal industrial policy is to set an investment subsidy when in product market competition firms play a Cournot output game, imply immediately that there hardly exists a robust industrial policy recommendation towards homogeneous goods industries.     

Non-discriminating renegotiation in a competitive insurance market

A variant of the Rothschild-Stiglitz model of a competitive insurance market is considered, where each uninformed firm is allowed to renegotiate the contracts that its customers initially sign, subject to the restriction that renegotiated contracts be offered to all the firm's customers. Such non-discriminating renegotiation is shown to weaken the profitability of cream skimming to the extent that there exists a unique equilibrium outcome. This outcome is that of Miyazaki and Spence i.e., the incentive-compatible pair of zero-profit contracts, if efficient; and the incentive-compatible, zero-profit pair of contracts maximizing low-risk utility, otherwise.     

Endogenous timing in private and mixed duopolies with emission taxes

This paper examines an endogenous timing game in product differentiated duopolies under price competition when emission tax is imposed on environmental externality. We show that a simultaneous-move (sequential-move) outcome can be an equilibrium outcome in a private duopoly under significant (insignificant) environmental externality, but this result can be reversed in a mixed duopoly. We also show that when environmental externalities are significant, public leadership yields greater welfare than private leadership, and that public leadership is more robust than private leadership as an equilibrium outcome. Finally, we find that privatization can result in a public leader becoming a private leader, but this worsens welfare.     

Contract renegotiation in a continuous state space

Summary. When players are unable to write complete state contingent contracts it is shown, within the context of a non-cooperative contracting-renegotiation game, that the only subgame perfect equilibrium allocations are those that correspond to the set of first-best allocations. Players are able to implement this set of allocations by signing an initial contract that is subsequently renegotiated in all states of the world. The contracting-renegotiation problem is complicated in an interesting way by assuming that the state space is continuous. The issue of the existence of an initial contract, that is subsequently renegotiated to the set of first-best allocations, must be resolved. Unlike Aghion, Dewatripont and Rey [1994], the results here do not require nor depend upon the comonotonicity of the objective functions. Received: January 27, 1995; revised version July 1, 1996     

Contract renegotiation and options in agency problems

This article discusses the ability of an agent and a principalto achieve the first-best outcome when the agent invests inan asset that has greater value if owned by the principal thanby the agent. When contracts can be renegotiated, a well-knowndanger is that the principal can hold up the agent, underminingthe agent's investment incentives. We begin by identifying acountervailing effect: Investment by the agent can increasehis value for the asset, thus improving his bargaining positionin renegotiation. We show that option contracts will achievethe first best whenever his threat-point effect dominates theholdup effect. Otherwise, achieving the first best is difficultand, in many cases, impossible.     

On the effects of emission standards as a non-tariff barrier to trade in the case of a foreign Bertrand duopoly: A note

Employing a model of an environmentally differentiated product market, we analyze how an emission regulation as non-tariff barriers to trade affects imports, the environment, and welfare in the case of a foreign Bertrand duopoly. Related to this issue, we reconsider the result of Moraga-González and Padrón-Fumero [Moraga-González, J.L., Padrón-Fumero, N., 2002. Environmental policy in a green market. Environmental and Resource Economics 22, 419–447] that a strict emission standard on a dirtier product degrades the environment and reduces the net social surplus associated with the valuation of environmental damage, if the marginal social valuation of environmental damage is larger. On the other hand, we show that a strict emission standard on a cleaner product always improves the environment and the net social surplus associated with the valuation of environmental damage.     

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

Bertrand Price Undercutting: A Brief Classroom Demonstration

The author presents a brief classroom demonstration illustrating Bertrand price undercutting. The demonstration is appropriate for micro principles and intermediate- and upper-level undergraduate classes, as well as graduate classes in micro, industrial organization, and game theory.     

Perpetual Leapfrogging in Bertrand Duopoly

We consider different patterns of infinite technological adoption choices by firms in a Bertrand duopoly. Every period technological progress provides a sequence of cost reducing innovations. The equilibrium concept is Markov perfect equilibrium. We analyze conditions for which equilibrium adoption leads to persistent leadership and those where firms alternate in adoption inducing leapfrogging. Only leapfrogging leads to technological improvement in the long run. Demand conditions play a crucial role in determining whether leapfrogging can be perpetual in Bertrand duopoly.     

Tax competition in a Bertrand model

We show that in Bertrand models pure-strategy equilibria exist only under extraordinarily restrictive assumptions. We analyze tax competition between two countries for foreign investment. In the symmetric case of equal gross profits of the firms, zero-taxation is the unique equilibrium in pure strategies. If gross profits differ between countries only -equilibria can exist. However, if the tax rate applies to foreign investment as well as to domestic sources no equilibria exist in pure strategies. The same holds true if countries compete for firms that differ in gross profit opportunities, unless extremely unrealistic conditions are met.     

A note on inertia in market share

In a simple model in which market share displays inertia, I show that a larger firm will always charge a higher price and make more profits than its smaller rival, but its market share will remain larger than its rival's.     

A note on Stackelberg competition

This note investigates a Stackelberg–Nash competition model. We determine the conditions under which the leaders may achieve better profits than the followers when all firms compete on quantity in a two stage game. We focus on the properties of the followers’ best response functions. It is shown that the Stackelberg equilibrium may coincide with the Cournot equilibrium. In addition, the followers may achieve higher profits than the leaders. Such results put forward the working and the consequences of strategic complementarities. These results are illustrated with three examples.     

A note on endogenous transfers

In a competitive and Walrasian stable world with two goods transfer paradoxes are very robust to endogenization (relating the size of the transfer to either the donor's or the recipient's GNP). Donor enrichment and/or recipient impoverishment occur in very general formulations of endogenization if and only if they occur in the model in which transfers are exogenous (as is usually assumed). Endogenization in practice will probably cause a dampening effect (smaller price and welfare changes than in the case of pure exogenous transfers).An earlier version of this paper was presented at the Econometric Society European Meeting in Munich, 1989, and EADI (European Association of Development Research and Training Institutes) in Oslo, 1990. We are grateful to an anonymous referee, Willem Buiter, Peter van Bergeijk, Richard Gigengack, Jan Pen, Georg Tillmann, Edward Towrr, and Casper de Vries for helpful comments.