This paper explores the role of inequity aversion as an explanation for observed behavior in experimental Cournot oligopolies. We show that inequity aversion can change the nature of the strategic interaction: quantities are strategic substitutes for sufficiently asymmetric output levels but strategic complements otherwise. We find that inequity aversion can explain why: some experiments result in higher than Cournot–Nash production levels while others result in lower, collusion often occurs with only two players whereas with three or more players (...) market outcomes are very close to Cournot–Nash, and players often achieve equal profits in asymmetric Cournot oligopoly. (shrink)

In cooperative Cournot oligopoly games, it is known that the β-core is equal to the α-core, and both are non-empty if every individual profit function is continuous and concave (Zhao, Games Econ Behav 27:153–168, 1999b). Following Chander and Tulkens (Int J Game Theory 26:379–401, 1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the γ-core, by two different approaches. The (...) first establishes that the associated Cournot oligopoly Transferable Utility (TU)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao’s core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the γ-core called Nash Pro rata (NP)-value. This result generalizes Funaki and Yamato’s (Int J Game Theory 28:157–171, 1999) core existence result from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity, and non-cooperative fairness. (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics (...) due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

In this article, we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand–Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered (...) for Nash equilibrium quantities and profits. Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms. Finally, we study a class of three-firm oligopolies with asymmetric costs in which the core inclusion property mentioned above still holds. We also provide numerical examples to illustrate the difficulty to generalize this result to an arbitrary number of firms because of negative equilibrium quantities. (shrink)

This paper presents a new theoretical justification for the Cournot–Bertrand model to arise in equilibrium when firms have, at the outset, the same cost structure and sell symmetrically differentiated products. The Cournot–Bertrand model assumes some firms compete on price, adjusting their production to meet demand, while others set quantities and let their price adjust until market equilibrium is reached. We show that this may occur endogenously due to the possibility of entry, which may be deterred when some of (...) the incumbents decide to set prices, while others free ride on this behavior and choose quantities. (shrink)

This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable under all (...) adaptive dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market. (shrink)

Pricing algorithms are computerized procedures a seller may use to adapt instantaneously its price to market conditions, including to prices quoted by its rivals. These algorithms are related to the extensive use of web-collectors which contribute in many industries to identifying the best price. In such settings, price competition operates between algorithms, no longer between executives of brick and mortar companies. In this context, the question is to know how implicit forms of collusion may arise between the sellers. This paper (...) is aimed at discussing this conceptual issue in a price-setting homogeneous product oligopoly with decreasing returns to scale where algorithms implement matching policies. Using fixed point argument, we find a family of equilibrium prices encompassing Cournot and Pareto efficient solutions, if matching is allowed upward and downward. Dynamical stability is studied in the linear demand constant return case. When matching operates only for price undercutting, this family is extended up to a bottom value of the market price, close to the Walrasian price. Pricing algorithms may solve the Bertrand–Edgeworth paradox. (shrink)

One is the very founding document of oligopoly theory, Cournot’s seminal work of 1838. This is both because the specific model that he presented has been much studied for its ability to generate complex dynamics and also because of its more general foreshadowing of game theory. It has often been noted that the Cournot equilibrium is but a special case of the Nash (1951) equilibrium, the more general formulation used by modern industrial organization economists in studying (...) class='Hi'>oligopoly theory. Indeed, it is sometimes even called the Cournot-Nash equilibrium. Although many of the models of complex oligopoly dynamics use the specific Cournot model, many use more general game theoretic formulations. We note simply as an aside here that Cournot’s work was the first to apply calculus to solving an economic optimization problem and also was the first to introduce supply and demand curves, albeit in the "Walrasian" form with price on the horizontal axis. (shrink)

This article provides a method for estimating the bounds of transaction costs in horizontal mergers. Consider, for example, a completed monopoly merger in linear Cournot oligopolies with 10 symmetric firms. The method shows that its transaction costs are at most 25% (78%) of total premerger profits if there is zero (100%) excess capacity. Such estimations can be extended in a straightforward manner to other mergers and other oligopoly models. The estimation is based both on the profitability precondition, and (...) on the non-empty core precondition, which postulates that the split of a merger’s profits be in its core. The article shows that the core in linear Cournot oligopolies has a non-empty interior, and indicates that the non-empty core precondition also sheds new lights on understanding important issues such as the stylized fact that mergers are likely to occur in markets plagued by excess capacities; why profitable mergers might not be formed; and why completed mergers might break up in the future. (shrink)

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. (...) We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return. (shrink)

Historians of philosophy have hitherto either given scant attention to Cournot and Renouvier’s views on scientific revolution, tried to read Kuhn’s concept of scientific revolution back into their works, or did not fully appreciate the extent to which these philosophers were reflecting on the works of their predecessors as well as on developments in mathematics and the sciences. Cournot’s views on cumulative development through revolution resemble Comte’s more than Kuhn’s, and his notion of progressive theoretical simplicity through revolution (...) recalls Whewell’s philosophy of science. Renouvier, far from regarding a scientific revolution as resulting in a new set of conceptual boxes imposing a conformity of thought on the scientific community, recognized that a new theory proposed during a revolution is open to more than one interpretation. (shrink)

The notion of Nash equilibrium in static oligopoly games is based on the assumption that each firm knows its entire demand curve (and, therefore, its entire profit function). It is much more likely, however, that firms only have some idea of the outcome of small price variations within some relatively small interval of prices. This is because firms can only learn their demand functions through price experiments and if they are risk-averse and/or have a low discount factor, they will (...) be unwilling to engage in extensive price experiments involving large variations in price. We can therefore expect firms to experiment through small price variations and stop when they reach a price such that no small deviation.. (shrink)

Augustin Cournot (1801-1877) a marqué l'histoire de la pensée économique en introduisant la modélisation des phénomènes économiques, et non leur seule quantification. Ce constat appelle une double question : 1° Comment la rupture opérée par Cournot s'inscrit-elle dans l'histoire et l'évolution des méthodes de l'économie? La question se pose d'autant plus que les Recherches sur les principes mathématiques de la théorie des richesses passèrent d'abord presque inaperçues. 2° Que reste-t-il aujourd'hui de ce tournant effectué par le «philosophe-géomètre»? Autrement (...) dit, comment penser l'actualité de l'œuvre économique de Cournot? Or, avant d'être un économiste, Cournot est d'abord mathématicien et philosophe. Comment son œuvre économique s'accorde-t-elle alors avec son activité de mathématicien, et comment prend-elle place dans sa réflexion philosophique, c'est-à-dire à la fois dans sa théorie de la connaissance et dans sa philosophie de l'action et de la décision? Comprendre la portée de l'œuvre économique de Cournot et sa place dans son œuvre multiforme, tel est le projet qui anime le présent ouvrage où économistes, philosophes, historiens des sciences et sociologue entrecroisent leurs approches de celui qui demeure l'un des économistes et des philosophes majeurs du XIXe siècle."--Page 4 of cover. (shrink)

This text reconsiders the philosophizing into the future of mankind and futurology done by molecular biologist Gunther Stent in *The Coming of the Golden Age* in the light of Raymond Ruyer's critical notice published in the aftermath of the publication of Stent's book in French translation. For Ruyer, it is an occasion to revisit his own take on what he called in his last work a "theology of the opposition between the organic and the rational," and to restate in a (...) new light his conclusions concerning Cournot's suggestion as to the becoming of social relationships in a context of management of complexity of association. It is argued here that both Stent and Ruyer share a common thermodynamic, informational, and also surprisingly Nietzschean ascendency in judging of the possible outcomes for the human race. (shrink)

According to Antoine Augustine Cournot, chance events are the result of the intersection between independent causal chains. This coincidental notion of chance is not a new one, but—as Cournot remarks—it comes from Saint Thomas Aquinas, Boethius, and more probably from Jean de La Placette. Such a conception of chance phenomena seems to be very important, not only because it is closely related to the Principle of Causality, but also since it grounds Cournot’s theory of objective probability. Starting (...) from Martin’s work, the main attempt of this survey is to endorse the idea that Cournot’s coincidental notion of hasard is objective, that is it is ontic and it does not depend—in some sense—on our degree of knowledge. In order to do that, a central role in the discussion will be given to the meaning of the independence between the intersecting causal chains and to Cournot’s conception of causation. (shrink)

C'est un ouvrage remarquable à bien des égards que Claude Ménard, qui est né au Québec en 1944 et a étudié en France l'histoire des sciences et l'économie avant d'enseigner l'histoire aux Pays-Bas, a récemment publié chez Flammarion sous le titre La formation d'une rationalité économique: A. A. Cournot. L'épistémologue des sciences sociales y trouvera une analyse intelligente et documentée d'une contribution qui occupe, par rapport à la formation de l'économie moderne, une place qui n'a probablement d'équivalent dans aucune (...) autre discipline. L'historien de la philosophie, tout autant que celui de l'économie, y appréciera l'éclairage neuf jeté sur l'œuvre d'un penseur dont l'importance a toujours été méconnue malgré le fait – ou peut-être plutôt à cause du fait – qu'au milieu du XIXe siècle, il se consacrait à des questions théoriques qui souvent n'allaient devenir importantes que pour les hommes du XXe siècle. L'historien des idées saura gré à l'auteur d'avoir su situer son analyse de la contribution de Cournot dans le contexte plus large des institutions et des idées qui ont fait du XIXe siècle le moment décisif de la reformulation moderne des idéologies. L'analyste des idéologies y trouvera donc aussi matière à réflexion puisque le rapport des sciences sociales et des idéologies y est abondamment discuté encore que, comme je chercherai à le montrer, le traitement proposé risque davantage, sur ce point, de laisser le lecteur sur sa faim. (shrink)

This paper seeks to rehabilitate the trade theory of Augustin Cournot. In contrast to the widespread awareness among neoclassical economists of Cournot's contribution to microeconomics, there is general ignorance of his trade theory, which an earlier generation of neoclassical theorists attributed to its erroneous conclusions. I dispute this view and attempt to show the internal consistency of Cournot's trade analysis. While the assumptions underpinning his trade theory could be considered extreme, they need to be understood in the (...) light of his methodological commitments, which included a rejection of utility in the theory of wealth, and a dismissal of Say's law regarding general employment. Furthermore, I argue that the assumptions underpinning neoclassical trade theory are no less extreme, even as their theoretical conclusions are (similarly) logically consistent. All of this serves to highlight the insufficiency of theoretical rigour in establishing the relevance of a theory; the importance of history of thought in reminding us that more than one theoretical perspective exists; and, of course, the indispensability of empirical engagement in trying to arbitrate between contrasting theoretical positions. (shrink)

A quadratic utility function is introduced in this paper to study the dynamic characteristics of Cournot duopoly game. Based on the bounded rationality mechanism, a discrete dynamical map that describes the game’s dynamic is obtained. The map possesses only one equilibrium point which is Nash point. The stability conditions for this point are analyzed. These conditions show that the point becomes unstable due to two bifurcation types that are flip and Neimark–Sacker. The synchronization property for that map is studied. (...) Through local and global analysis, some dynamics of attracting sets are investigated. This analysis gives some insights on the basis of those sets and the shape of the critical curves. It also shows some lobes found in those attracting sets which are constructed due to the origin focal point. (shrink)

This book provides both an explanation of the inflation which has bedeviled economic policy in the West since the end of World War II and a micro-economic theory to purge Keynesian models of the Walrasian strain derived from Marshall's Principles. By focusing on what is taken to be the representative business firm of the twentieth century - the large corporation or megacorp - the microeconomic model presented in the book reverses the usual assumptions of economic analysis. Instead of assuming the (...) existence of firms with no control over prices, the book examines how the megacorp uses its pricing power to finance its own internal rate of growth. The result is a determinant model of how prices are set under the sort of oligopolistic conditions which prevail in most modern industries throughout the world. (shrink)