Technology choice in an evolutionary oligopoly game

In this paper, we propose and analyze a two-stage oligopoly game in which firms first simultaneously choose production technologies and in the second stage simultaneously choose production quantities. After characterizing the Nash equilibrium of the game, we cast our static model in a dynamic setting exploring the stability properties of the market equilibrium in two different cases: (i) exogenously distributed technologies and Cournot adjustments and (ii) endogenously distributed technologies in an infinite population game with Cournot–Nash equilibrium outputs. The main aim of the paper is that of extending the results about Cournot oligopoly stability in an evolutionary setting of heterogeneous decreasing returns-to-scale technologies. We show how the interplay between production decisions and R&D decisions can generate endogenous market fluctuations leading to complex dynamic phenomena.     

The role of information in profit-maximizing and labor-managed duopoly models

This paper analyzes the welfare implications of acquiring information for profit-maximizing and labor-managed duopolies. We invent a unified method of exploring the role of information in a two-person game under uncertainty on the basis of comparative static analysis, and then apply the method to both the PMF and the LMF. It is shown that whereas the LMF's behavior is analogous to that of the PMF twin in some circumstances, the former may be entirely different from the latter in others. Because a special status is accorded to labor as a variable factor of production, the informational analysis of the LM economy requires special care for both computations and interpretations.     

Advertising conjectures and the nature of advertising competition in an oligopoly

We estimate advertising conjectural variations within a simultaneous system that includes advertising and demand equations for cigarette manufacturers. This allows insight into advertising decisions in an oligopoly. The advertising conjectures are positive and statistically significant, indicating that firms do not hold Cournot conjectures as is usually assumed in theoretical models. Instead, firms perceive that their rivals will respond directly to their own advertising. We also find evidence that, while cigarette advertising rearranges market share by increasing firm-level demand relative to rivals' demand, it also increases market demand for cigarettes. Hence there are positive spillovers from advertising in the cigarette industry.     

An evolutionary model with best response and imitative rules

We formulate an evolutionary oligopoly model where quantity setting players produce following either the static expectation best response or a performance-proportional imitation rule. The choice on how to behave is driven by an evolutionary selection mechanism according to which the rule that brought the highest performance attracts more followers. The model has a stationary state that represents a heterogeneous population where rational and imitative rules coexist and where players produce at the Cournot–Nash level. We find that the intensity of choice, a parameter representing the evolutionary propensity to switch to the most profitable rule, the cost of the best response implementation as well as the number of players have ambiguous roles in determining the stability property of the Cournot–Nash equilibrium. This marks important differences with most of the results from evolutionary models and oligopoly competitions. Such differences should be referred to the particular imitative behavior we consider in the present modeling setup. Moreover, the global analysis of the model reveals that the above-mentioned parameters introduce further elements of complexity, conditioning the convergence toward an inner attractor. In particular, even when the Cournot–Nash equilibrium loses its stability, outputs of players little differ from the Cournot–Nash level and most of the dynamics is due to wide variations of imitators’ relative fraction. This describes dynamic scenarios where shares of players produce more or less at the same level alternating their decision mechanisms.     

Evolutionary competition in a mixed market with socially concerned firms

In this paper we study an oligopoly market where profit-maximizing firms and socially concerned firms compete in quantities. Confronting remarks by Milton Friedman and Gary Becker, we are using an evolutionary setting to investigate the endogenous choice of the proper objective of business firms and the influence of product differentiation on the long run survival of firms which pursue non-profit motives. We find that firms which consider a combination of profit and consumer welfare can indeed have larger market shares and profits than their profit-maximizing rivals. One insight is that it might pay off for shareholders to consider stakeholder welfare, but that the level of social concern should not be too high. Based on a strategy׳s profitability, we consider asynchronous evolutionary updating with firms selecting Nash quantities or choosing best replies to the expected market quantity. Here we observe that the consumers׳ willingness to pay a price premium for products is crucial for the long run survival of socially concerned firms. Depending on the degrees of product differentiation and social concern, long run outcomes consist either of both types of firms or only one type of firm. If the firms׳ propensity to switch between a social or a profit-maximizing strategy is sufficiently large, steady states are unstable and even complicated dynamics can occur.     

Robust results on the sharing of firm-specific information: Incentives and welfare effects

Contrary to much of the existing literature, we obtain robust and clear-cut results for the incentives and welfare effects of information sharing when information is firm-specific. We show that firms’ incentives to share this type of information are aligned with social welfare. Whenever revealing information is the dominant strategy (such as for Cournot firms revealing costs or Cournot and Bertrand firms revealing demand), it is socially beneficial. Only cost information in Bertrand competition will not be revealed but this is socially desirable, too. These findings are independent of distributional assumptions on random shocks and signals and hold for general asymmetric oligopoly with any mixture of substitute, complementary and independent goods.     

Strategic location choice under dynamic oligopolistic competition and spillovers

This paper investigates firms׳ optimal location choices explicitly accounting for the role of inwards and outwards knowledge spillovers in a dynamic Cournot oligopoly with firms that are heterogeneous in their ability to carry out cost-reducing R&D. Firms can either locate in an industrial cluster or in isolation. Technological spillovers are exchanged between the firms located in the cluster. It is shown that a technological leader has an incentive to locate in isolation only if her advantage exceeds a certain threshold, which is increasing in firms׳ discount rate, in industry dispersion, and in the intensity of knowledge spillovers. Scenarios are identified where although it is optimal for the technological leader to locate in isolation, from a welfare perspective it would be desirable that she locates in the cluster.     

Cooperative and noncooperative R&D with spillovers: The case of labor-managed firms

This research focuses on the behavior of not-for-profit enterprises. In particular, using a familiar model of cost-reducing R&D with spillovers, we examine strategic interactions between labor-managed firms in a duopoly. Research spillovers have not been previously considered in the context of labor-managed firms. Among four market scenarios involving (i) competition in research and production; (ii) cooperation in research and production; (iii and iv) competition or cooperation in research and the reverse in production, our results show that research is greatest under full cooperation, while output is greatest under full competition. Output and R&D are the lowest in the case when firms compete in research, but form a production cartel. The degree of research spillovers has a crucial bearing upon these rankings. Some of these results differ from those for profit-maximizing firms. The effects of changes in research spillovers on employment (output) are shown to depend upon the nature of the underlying production technology. Policy implications are discussed.     

Firm heterogeneity and wages in unionised labour markets: Theory and evidence

In many countries wages are set in two stages, where industry-level collective bargaining is followed by firm-specific arrangements determining actual paid wages as a mark-up on the industry wage floor. What explains the wage set in each of these stages? In this paper we show that both the industry wage floor and the average wage cushion are systematically associated with the degree of firm heterogeneity in the industry: The former (latter) is negatively (positively) associated with the productivity spread. Furthermore, since the response of the wage floor dominates that of the wage cushion, workers in more heterogeneous industries tend to get lower actual paid wages. These conclusions are reached in a model of Cournot oligopoly with firm productivity heterogeneity and a two-tiered wage setting system. They are then confirmed by administrative data covering virtually all workers, firms and collective bargaining agreements of the Portuguese private sector for the period 1991–2000.     

OLIGOPOLY GAMES AND THE COURNOT–BERTRAND MODEL: A SURVEY

Traditional oligopoly models hold that firms compete in the same strategic variable, output (Cournot) or price (Bertrand). Alternatively, a hybrid model allows some firms to compete in output and other firms to compete in price, also known as the Cournot–Bertrand model. When the choice of strategic variable is endogenous, the established dominant strategy is output competition. A growing body of work demonstrates, however, that the Cournot–Bertrand outcome can be a subgame‐perfect Nash equilibrium in the presence of market asymmetries. Observations of real‐world markets consistent with Cournot–Bertrand behavior bolster justification for the model and have stimulated an impressive and evolving literature on advances and applications. We lay out the roots of the Cournot–Bertrand model and explore a number of model developments. We categorize 12 primary models in the literature based on alternative assumptions. In particular, some authors consider when the timing of play as well as the choice of strategic variable are endogenous. Altogether, this research identifies when Cournot–Bertrand behavior can emerge in a dynamic setting and under alternative market conditions. We also review the Cournot–Bertrand model applications in the fields of international economics, industrial organization, labor, and public economics. We expect the literature to continue to expand in the future.     

Cournot oligopoly models with time delays

In this paper a system of competing firms is considered in which adjustments of output are subject to delays. Under the Cournot strategy, stability of the oligopoly problem is considered. If each firm calculates its optimal output based on a knowledge of its own production at that time, and of its competitor's outputs at a previous time, stability is not affected by the information delays. However, if all the information available to each firm is subject to a delay, then stability is affected, and the likelihood of stability increases with decreasing delays.     

The impact of lead time on capital investments

We study equilibrium investment strategies of firms competing in stochastic dynamic market settings and facing two types of investment structures: investment with significant lead time (or time-to-build) and investment without (or minor) lead time. We investigate how investment behavior changes when investment is subject to time-to-build versus when it is not. We characterize equilibrium investment strategies under several information structures and compare results to the social optimum. We offer some new results. The model predicts that, controlling for demand, and production and investment costs, investments and outputs can be higher in progressive industries (which often exhibit time-to-build) than in fast-paced industries (where time-to-build is insignificant). Furthermore, for both investment types (investment with or without time-to-build) we offer a novel equilibrium in which firms incrementally invest. This behavior is driven by demand uncertainty and capacity constraints. Also, expected outputs are lower than Cournot outputs as firms face uncertainty. Moreover, the amount of uncertainty has different effects over investment types.     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

Rivalry Restraint as Equilibrium Behavior

Rivalry restraint has received a lot of attention as a theory of profits in recent research on business strategy. Its economic rationale is explained as the consequences of either exogenous or endogenous anticompetitive forces present in different industries. In this paper, we use a dynamic oligopolistic industry model and show that rivalry restraint emerges as equilibrium behavior among firm owners who delegate decisions to managers. In the corresponding two‐stage game, managers choose optimal production rates in a dynamic Cournot market and owners set incentives for managers, acting sequentially rational. Equilibrium incentives correspond to rivalry restraint, that is, managers are less aggressive in the product market with lower outputs and increasing profits for all firms in the industry.     

-learning agents in a Cournot oligopoly model

Q-learning is a reinforcement learning model from the field of artificial intelligence. We study the use of Q-learning for modeling the learning behavior of firms in repeated Cournot oligopoly games. Based on computer simulations, we show that Q-learning firms generally learn to collude with each other, although full collusion usually does not emerge. We also present some analytical results. These results provide insight into the underlying mechanism that causes collusive behavior to emerge. Q-learning is one of the few learning models available that can explain the emergence of collusive behavior in settings in which there is no punishment mechanism and no possibility for explicit communication between firms.     

Regulation of road accident externalities when insurance companies have market power

Accident externalities that individual drivers impose on one another via their presence on the road are among the most important external costs of road transport. We study the regulation of these externalities when insurance companies have market power. Some of the results we derive have close resemblance to the earlier literature on externality regulation with market power in aviation and private roads, but there are important differences, too. Using analytical models, we compare the first-best public welfare-maximizing outcome with a private profit-maximizing monopoly, and oligopoly. We find that insurance companies will internalize some of the externalities, depending on their degree of market power. We derive optimal insurance premiums, and regular parametric taxes as well as “manipulable” ones that make the companies set socially optimal premiums. The latter take into account that the firm tries to exploit knowledge of the tax rule applied by the government. Finally, we also study the taxation of road users rather than that of firms.     

Oligopolistic and competitive behavior of spatially separated markets

We examine the connection between Cournot oligopoly and perfect competition by showing that a fairly general oligopoly model with spatially separated markets generates a general spatial price equilibrium model as an extreme, limiting case. Our analysis depends crucially on the fact that the governing equilibrium conditions of both the oligopoly and the spatial price equilibrium problem can be formulated as variational inequalities.     

Imitators and optimizers in Cournot oligopoly

We analyze a symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round à la Vega-Redondo, F., [1997. The evolution of Walrasian behavior. Econometrica 65, 375–384]. Optimizers play a myopic best response to the opponents’ previous output. Firms make mistakes and deviate from their decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers.     

Workers’ enterprises are not perverse: differential oligopoly games with sticky price

We take a differential game approach to study the dynamic behaviour of labour managed (LM) firms, in the presence of price stickiness. We find that the oligopoly market populated by LM firms reaches the same steady state equilibrium allocation as the oligopoly populated by profit-maximising (PM) firms, provided that the LM membership and the PM labour force are set before the market game starts. The conclusion holds under both the open-loop solution and the closed-loop solution. The result confirms the point made by Sertel (Eur Econ Rev 31:1619–1625, 1987) in a static framework.     

Technology ladders and R&D in dynamic Cournot markets

Motivated by dramatic and unpredictable technological advances in energy production (for instance drilling and extraction of shale oil), we extend Cournot models of competition to incorporate research and development (R&D) that can lead to (stochastic) drops in production costs. Our model combines features of patent racing with dynamic market structure, capturing the interplay between the immediate competition in terms of production rates and the long-term competition in R&D. The resulting Markov Nash equilibrium is found from a sequence of one-step static games arising between R&D successes, and several numerical examples and extensive analysis of the emerging comparative statics are presented. Analyzing the relationship between current market dominance and the level of R&D investments, we find that market leaders tend to invest more, which in some sense makes oligopoly dynamically unstable. We show that anticipated market transitions have long-term impact; for example the potential of future monopoly can spur R&D investment now, even if the firm is presently uncompetitive and not actively producing. We also show that, surprisingly, random innovations have an ambiguous effect on R&D. This feature, which is driven by the Cournot framework, contrasts with the common situation whereby uncertainty lowers innovation and delays R&D investments. Finally, we demonstrate that increased competition may actually increase efforts to innovate through higher desire to achieve dominance. This would match the anecdotal evidence that the threat of market entrants forces incumbents to maintain high R&D.