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)

Economists use various models to explain why it is that firms are capable of pricing above marginal cost. In this paper, we will examine two of them: the Cournot and Bertrand duopoly models. Economists generally accept both models as good explanations of the phenomenon, but the two models contradict each other in various important ways. The puzzle is that two inconsistent explanations are both regarded as good explanations for the same phenomenon. This becomes especially worrisome when the two models (...) are offering divergent policy recommendations. This report presents that puzzle by laying out how the two models contradict each other in a myriad of ways and then offers five possible solutions to that puzzle from various economists, philosophers of science, and philosophers of economics. (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)

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)

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)

Die Ausgabe der Oeuvres Complètes von A. A. Cournot erlaubt es, den Umfang und den genauen Stellenwert, die der Lektüre von Leibniz und dem Nachdenken über seine Gedanken in der Entwicklung des Autors zukommen, zu bestimmen. Eine vollständige Untersuchung würde ein Buch füllen. 1. Zunächst möchten wir hervorheben, daß Cournot Leibniz in beachtlichem Maße verpflichtet ist. Die Leibniz-Bezüge durchziehen die Werke von Cournot nicht nur, sondern sie verleihen ihnen ein fundamentales Gerüst. Er beruft sich auf die Ausgaben (...) der Primärliteratur, die um die Mitte des 19. Jahrhunderts zur Verfügung standen: Des Maizeaux, Raspe, Dutens, den Briefwechsel mit Arnauld und mit Clarke, das Specimen dynamicum, das Système nouveau, die Nouveaux Essais, die Théodicée usw. Zwei Kapitel sind Leibniz gewidmet: eins bei der Untersuchung der Systeme in §§ 381-392 des Essai, ein anderes handelt über Newton, Leibniz und Locke. Diese Präsenz ist nicht nur historischer, sondern philosophischer, wissenschaftlicher und kritischer Natur. Leibniz' Lehren befruchten Cournots Denken. 2. Umgekehrt können wir sagen, daß Leibniz Cournot wenigstens im gleichen Maße verpflichtet ist. Indem Cournot Leibniz' Gedanken unter vielfältigen Aspekten angeht, trägt er zur Präzisierung ihrer Interpretation bei. Aber es sind nicht nur gelehrte Kommentare, was die Aufmerksamkeit auf sich zieht, Leibniz' Thesen sind vielmehr weitergeführt und zu neuem Leben erweckt, sie sind konfrontiert mit dem Wissen und der Kultur des 19. Jahrhunderts, sie treten ein in das intellektuelle Kapital der Zeit Cournots. Cournot hat ebensoviel für Leibniz getan wie Leibniz für Cournot; denn er hat die wissenschaftlichen Thesen von Leibniz über die Algebra, die Geometrie und die Wahrscheinlichkeit weitergeführt, er hat die Lehren über die Substanz, die Kraft und den zureichenden Grund erneuert und -was noch wichtiger ist — er hat von einigen Gedanken Leibnizens aus die Grundlagen der ökometrie erarbeitet. 3. Jetzt, im November 1980, verfügen wir über die Gesamtheit der Bände der Oeuvres Complètes, die der Philosophie und der Ökonomie gewidmet sind. Wir begrenzen daher diesen ersten Aufsatz auf Fragen, die dort herausgearbeitet sind. Für einen zweiten Aufsatz, welcher sich auf die in Arbeit befindlichen Bände der Mathematik stützen wird, lassen wir die im engeren Sinne wissenschaftlichen Gesichtspunkte des Werkes von Cournot in ihren Beziehungen zu denen von Leibniz zurück 1. (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)

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)

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)

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)

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)

Dans un article décisif sur la naissance du calcul des probabilités (1970), Ernest Coumet rappelait la formule de Cournot selon laquelle le retard qui marque la naissance de la théorie du hasard est «un pur effet du hasard». On se propose ici de soumettre ce jugement à l'examen critique non de l'histoire, mais de la pensée même de Cournot; sa philosophie de l'histoire et sa représentation de l'histoire des sciences au XVIIe siècle semblant, tout d'abord, dénoncer par avance (...) un jugement aussi péremptoire. Pour rendre compte de ce qui peut alors apparaître de sa part comme une inconséquence, voire un aveuglement, on forme l'hypothèse que cette affirmation constitue un artefact de sa conception internaliste de l'histoire des sciences et des révolutions scientifiques. En ce sens, larticle constitue une illustration de la nécessité théorique, mais aussi des difficultés de l'histoire des mathématiques. (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)

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)

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 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)

The comparison between two nonlinear duopoly models constructed based on symmetric utility function that is derived from Cobb–Douglas is investigated in this paper. The first model consists of two firms which update their outputs using gradient-based mechanism called bounded rationality. The second model contains a bounded rational firm that is competing with a firm whose outputs depend on a trade-off between market share maximization and profit maximization. For the two models, the fixed points are calculated and their conditions of stability (...) are analyzed. The obtained results show that the second model is more stabilizing provided that the second firm adopts low weights of trade-offs. We show that the two models can be destabilized via flip bifurcation only. Furthermore, the noninvertibility of the two models that can give rise to several stable attractors is discussed. (shrink)

It is a common opinion that chance events cannot be understood in causal terms. Conversely, according to a causal view of chance, intersections between independent causal chains originate accidental events, called “coincidences”. Firstly, this book explores this causal conception of chance and tries to shed new light on it. Such a view has been defended by authors like Antoine Augustine Cournot and Jacques Monod. Second, a relevant alternative is provided by those accounts that, instead of acknowledging an intersection among (...) causal lines, claim to track coincidences back to some common cause. Third, starting from Herbert Hart and Anthony Honoré’s view of coincidences (Causation in the Law. Clarendon Press, Oxford, 1959). This book provides a more detailed account of coincidences, according to which coincidental events are hybrids constituted by ontic (physical) components, which is the intersection between independent causal chains, plus epistemic aspects, including but not limited to, access to information, expectations, relevance, significance, desires, which in turn are psychological aspects. -/- The main target of the present work is to show that the epistemic aspects of coincidences are, together with the independence between the intersecting causal chains, a constitutive part of coincidental phenomena. This book aims to introduce and discuss recent work in psychology concerning one’s judgment about coincidences; this data offers further materials and reasons to reflect upon our understanding of coincidences and to refine our hybrid conception. (shrink)

To reveal the mechanisms of firms’ technological strategic choices between innovation and imitation, an evolutionary game model is proposed from the perspective of the behavioral biases. First, behavioral biases such as reference point dependence, loss aversion, and probability weighting can be defined and modeled based on the prospect theory. Second, according to the firm theory, a Cournot or Stackelberg game modeled with a technology spillover effect and intellectual property protection is applied to portray the interaction between firms. Third, an (...) improved evolutionary game model is provided by incorporating behavioral biases into the framework of the decision-making process. Finally, the simulation analysis of some important factors, such as intellectual property protection, patent fees, innovation risks, decision-making attitudes, and consumers’ price preference on firms’ technological strategic choices, is presented. The corresponding results show that innovation risk is an important factor affecting the technological strategic choices of firms, increasing the intellectual property protection and the patent fee for technology transfer can effectively control the spillover effect of technology, there is a partial U-shaped relationship between the consumers’ price preference and innovation, and the behavioral biases such as reference point dependence, loss aversion, and probability weighting will change the perception of payoff and risk and will eventually induce firms to adopt the innovation strategy. (shrink)

We study an extension of Stackelberg’s model in which many firms can produce at many different times. Demand is affine, while cost is linear. In this setting, we investigate whether Stackelberg’s results in a two-firm game are robust when the number of firms increases. We show that firms may not need to anticipate further entries, leaders might earn less than in the simultaneous game, and, whatever its cost and its time of entry, the firm’s entry always improves welfare.

The term “Renaissance” usually applies to a period in European history during which the Greco-Latin culture was rediscovered and modern science started. We show that “the Idea of Renaissance” indicates a universal process: a community (a nation, for example), identifying needs that it does not know how to satisfy by itself, and recognising that another community already satisfies them, tries first to acclimate the external process, and then becomes a creative entity. Several interpretations of this process have already been given: (...) we study three of them: the law of the three states by Auguste Comte, the notion of “a single revolution” in Kant’s Critic of Pure Reason and Critic of Judgement, and the notion of “scientific revolution” by A. A. Cournot. Thus conceived, Renaissance means a challenge in which all cultures are equally involved: discovering, even elsewhere, the means of satisfy needs which are related to scientific knowledge and know-how; trying to assimilate them; and making them productive and indigenous by becoming creative. (shrink)

A summary is provided of Ruyer's important contribution, also a reversal from some conclusions held in his secondary doctoral dissertation, about the limits inherent in technological progress, and an attempt is made to show the coherence of this position to Ruyer's metaphysics. Simondon's response is also presented, and subsequently analyzed especially as it culminates in a concept of concretizations. As Simondon indicated, and with a displacement in Ruyer's limitating framework on unconditional growth, we end up searching for what represents the (...) category of the ultimate for those two philosophers of the cyberworld. (shrink)

Technology licensing as a vital part of business behavior in many industries has drawn a fair amount of attention in industrial organization literature. Most existing literature on licensing decisions assumes that all firms engage in Cournot or Bertrand competition, while the type of mixed competition may affect the choice of the licensor. In this context, what decision will the licensor make faced with different mixed competitions? This paper studies the optimal technology licensing contract of a licensor firm engaging in (...) different mixed competitions with a potential licensee in a differentiated duopoly market considering one upstream firm that provides key inputs. We find that if either the royalty or fixed-fee licensing is applied, the licensor favors royalty licensing under Bertrand-Cournot competition when the degree of substitution is small and prefers the fixed-fee licensing no matter under what kind of mixed competition as the degree of substitution increases. In the case of fixed-fee licensing, the result shows that the profits of licensors are the same under different types of mixed competition. Besides, fixed-fee licensing is not always the optimal choice for consumers, and they would prefer royalty licensing when the degree of substitution is very small. (shrink)

This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of rationalizable strategies (...) are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game. (shrink)

We exploit the properties of homogeneous functions to characterize the symmetric pure-strategy Nash equilibria of n-player symmetric games in which each player’s revenue function is not homogeneous but it can be decomposed into the sum of homogeneous functions with different degrees of homogeneity. Our results aim to provide a pathway for an easy computation of symmetric equilibria for this type of games. We discuss our results in a Cournot game, a contest game, and a public good game.

Présentation de la spécificité de l'épistémologie en France, entre philosophie de la connaissance et philosophie des sciences, à travers un panorama de son histoire depuis la fin du XIXe siècle, de ses grands courants et de ses grandes figures : A. Comte, A. Cournot, C. Bernard, G. Bachelard, H. Poincaré, etc.