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Limited knowledge of demand and oligopoly equilibria
Abstract
In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.
... This note proves the existence of a first-order locally consistent equilibrium (see, for example, BONANNO and ZEEMAN [1985], GARY-BOBO [1989a], [1989b) with more general strategy spaces and without the "boundary conditions" employed by BONANNO and ZEEMAN [1985]. Two examples of application are also provided. ...
... This note proves the existence of a first-order locally consistent equilibrium (see, for example, BONANNO and ZEEMAN [1985], GARY-BOBO [1989a], [1989b) with more general strategy spaces and without the "boundary conditions" employed by BONANNO and ZEEMAN [1985]. Two examples of application are also provided. ...
... A first-order locally consistent equilibrium (1-LCE) of a game is a configuration of strategies at which the first-order condition for pay-off maximization is simultaneously satisfied for all players (see SILVESTRE [1975], BONANNO and ZEEMAN [1985], GARY-BOBO [1987], [1989a], [1989b]). The economic motivation for introducing this equilibrium concept is that oligopolistic firms do not know their effective demand function, but "at any given status quo each firm knows only the linear approximation of its demand curve and believes it to be the demand curve it faces" (BONANNO and ZEEMAN (1985, p. 277)). ...
This note proves the existence of a first-order locally consistent equilibrium (see, for example, Bonanno and Zeeman [1985], Gary-Bobo [1989a], [1989b]) with more general strategy spaces and without the "boundary conditions" employed by Bonanno and Zeeman [1985]. Two examples of application are also provided. /// Cette note prouve l'existence d'un équilibre localement cohérent du premier ordre (voir, par exemple, Bonanno et Zeeman [1985], Gary-Bobo [1989a], [1989b]) avec des espaces de stratégies plus générales et sans la "condition de frontière" employés par Bonanno et Zeeman. Deux exemples d'application en économie sont aussi donnés.
... Farahat and Perakis (2010) propose the use of a linear demand function for markets with differentiated products. Furthermore, manufacturers frequently gain information about the type of market demand function through price experiments, which are observed over a restricted range to prevent losing existing customers (Silvestre 1977, Bonanno andZeeman 1985). As Silvestre (1977) and Bonanno and Zeeman (1985) state, manufacturers run price experiments to achieve local, linear approximations of demand. ...
... Furthermore, manufacturers frequently gain information about the type of market demand function through price experiments, which are observed over a restricted range to prevent losing existing customers (Silvestre 1977, Bonanno andZeeman 1985). As Silvestre (1977) and Bonanno and Zeeman (1985) state, manufacturers run price experiments to achieve local, linear approximations of demand. In the U.S. pediatric vaccine market, the annual change in the price of each vaccine is negligible (see CDC 2014a, b). ...
Pricing strategies in the U.S. pediatric vaccines market are studied using a Bertrand-Edgeworth-Chamberlin price game. The game analyzes the competition between asymmetric manufacturers with limited production capacities and linear demand, producing differentiated products. The model completely characterizes the unique pure strategy equilibrium in the Bertrand-Edgeworth-Chamberlin competition in an oligopoly setting. In addition, the complete characterization of mixed strategy equilibrium is provided for a duopoly setting. The results indicate that the pure strategy equilibrium exists if the production capacity of a manufacturer is at their extreme. For the capacity regions where no pure strategy equilibrium exists, there exists a mixed strategy equilibrium. A duopoly setting provides the distribution functions of the mixed strategy equilibrium for both manufacturers. The proposed game is applied to the U.S. pediatric vaccine market, in which a few asymmetric vaccine manufacturers produce differentiated vaccines. The source of differentiation in the competing vaccines is the number of medically adverse events, the number of different antigens, and special advantages of those vaccines. The results indicate that the public sector prices of the vaccines are higher than the vaccine equilibrium prices. Furthermore, the situation when shortages of certain pediatric vaccines occur is studied. Market demand and degree of product differentiation are shown as two key factors in computing the equilibrium prices of the vaccines.
... Ideally, stipulation of a demand system should be based upon consumer theory and supported by empirical indication (Farahat and Perakis, 2010). Manufacturers often learn about the market demand function through price experiments (Silvestre, 1977;Bonanno and Zeeman, 1985). Such price experiments are performed in a narrow range to avoid losing existing customers. ...
... Such price experiments are performed in a narrow range to avoid losing existing customers. As Silvestre (1977) and Bonanno and Zeeman (1985) claim, manufacturers perform price experiments to obtain local, linear approximations of demand. In the United States pediatric vaccine market, each year the change in the price of a vaccine produced by a manufacturer is small (Centers for Disease Control and Prevention, 2014a, 2014b). ...
The United States pediatric vaccine market is examined using Bertrand-Edgeworth-Chamberlin price competition. The proposed game captures interactions between symmetric, capacity-constrained manufacturers in a differentiated, single-product market with linear demand. Results indicate that a unique pure strategy equilibrium exists in the case where the capacities of the manufacturers are at their extreme. For the capacity region where no pure strategy equilibrium exists, there exists a mixed strategy equilibrium where the distribution function, its support, and the expected profit of the manufacturers are characterized. Three game instances are introduced to model the United States pediatric vaccine market. In each instance, the manufacturers are assumed to have equal capacity in producing vaccines. Vaccines are differentiated based upon the number of reported adverse medical events for that vaccine. Using the game theoretic model, equilibrium prices are computed for each monovalent vaccine. Results indicate that the equilibrium prices for monovalent vaccines are lower than the federal contract prices. The numerical results provide both a lower and upper bound for the vaccine equilibrium prices in the public sector, based on the capacity of the vaccine manufacturers. Results illustrate the importance of several model parameters such as market demand and vaccine adverse events on the equilibrium prices.
... They call ''optimally imperfect decisions'' the decisions such that ''The calculation of the appropriate decision is simple, inexpensive, and well suited for frequent repetition''. This point of view is also shared by other authors, see [30] [11] [12]. ...
... They call ''optimally imperfect decisions'' the decisions such that ''The calculation of the appropriate decision is simple, inexpensive, and well suited for frequent repetition''. This point of view is also shared by other authors, see [30,11,12]. In this paper we consider an industry where n firms, indexed by i = 1,. . . ...
We consider a Cournot oligopoly game, where firms produce an homogenous good and the demand and cost func-tions are nonlinear. These features make the classical best reply solution difficult to be obtained, even if players have full information about their environment. We propose two different kinds of repeated games based on a lower degree of rationality of the firms, on a reduced information set and reduced computational capabilities. The first adjustment mechanism is called ''Local Monopolistic Approximation'' (LMA). First firms get the correct local estimate of the demand function and then they use such estimate in a linear approximation of the demand function where the effects of the competitorsÕ outputs are ignored. On the basis of this subjective demand function they solve their profit maxi-mization problem. By using the second adjustment process, that belongs to a class of adaptive mechanisms known in the literature as ''Gradient Dynamics'' (GD), firms do not solve any optimization problem, but they adjust their pro-duction in the direction indicated by their (correct) estimate of the marginal profit. Both these repeated games may con-verge to a Cournot–Nash equilibrium, i.e. to the equilibrium of the best reply dynamics. We compare the properties of the two different dynamical systems that describe the time evolution of the oligopoly games under the two adjustment mechanisms, and we analyze the conditions that lead to non-convergence and complex dynamic behaviors. The paper extends the results of other authors that consider similar adjustment processes assuming linear cost functions or linear demand functions.
... pathological and robust examples can be found in e.g. Roberts and Sonnenschein, 1977, Friedman, 1983 and Bonanno, 1988). A way out of this problem is to consider equilibria along the lines of Bonanno and Zeeman (1985) and Bonanno (1988). They study price setting oligopolies where all Þrms have constant marginal costs, that is C i (x i ) = c i x i . Bonanno and Zeeman (1985) consider the case where producers only focus on the Þrst order conditions for an optimum, that is, a price vector p * = (p * 1 , . . . , p * n ) is called an equilibrium when ...
... It is easily veriÞed that any Þxed point p * = (p * 1 , p * 2 , . . . , p * n ) of (6) satisÞes the Þrst order conditions for a Bertrand-Nash equilibrium, and hence corresponds to an equilibrium in the sense of Bonanno and Zeeman (1985), see the discussion in Section 2. We are interested in the stability of these equilibria. We have the following result (recall that D i jk (p) ≡ ∂ 2 D i (p) ∂p j ∂p k ...
We consider a price adjustment process in a model of monopolistic compe-tition. Firms have incomplete information about the demand structure. When they set a price they observe the amount they can sell at that price and they observe the slope of the true demand curve at that price. With this information they estimate a linear demand curve. Given this estimate of the demand curve they set a new optimal price. We investigate the dynamical properties of this learning process. We Þnd that, if the cross-price effects and the curvature of the demand curve are small, prices converge to the Bertrand-Nash equilibrium. The global dynamics of this adjustment process are analyzed by numerical sim-ulations. By means of computational techniques and by applying results from homoclinic bifurcation theory we provide evidence for the existence of strange attractors.
... Then, we are in a twodimensional problem and it is readily verified that firm A's profit evaluated at the deviation is given by t n (5+t i Ât n ) 2 Â144. 5 Since the profit at the initial configuration is equal to t i Â2, it is a matter of simple calculation to check that the deviation proposed is always strictly profitable when t n >2.464t i . The result then follows from the inequality max[:(n), ;(n)]>2.464. ...
... The same idea underlies the work of Bonanno[4], Bonanno and Zeeman[5], and Gary-Bobo[13]. ...
Lancasterian models of product differentiation typically assume a one-dimensional characteristics space. We show that standard results on prices and locations no longer hold when firms compete in a multi-characteristics space. In the location game with n characteristics, firms choose to maximize differentiationin the dominant characteristic and to minimize differentiationin the others when the salience coefficient of the former issufficiently large. Thus, the principle of minimum differentiationholds for all but one characteristic. Furthermore, prices donot necessarily fall when products get closer in the characteristicsspace because price competition is relaxed when products aredifferentiated enough in the dominant characteristic. Journalof Economic Literature Classification Numbers: L1, M3, R3. Copyright 1998 Academic Press.
... A complementary approach has been adopted in Bischi and Baiardi (2015b), where the authors critically discuss the assumption, often considered in economic theory, of the existence of a representative agent, according to which identical or quasi identical players behave in identical or quasi identical ways (see, e.g., Kirman 1992;Aoki 1998;Bischi et al. 1999 for discussions on the topic). To this end, in the first part of that work, the authors account for three different dynamic adjustment processes belonging to the class of market share attraction models (see, e.g., Bell et al. 1975;Bonanno and Zeeman 1985;Carpenter et al. 1988;or Farris et al. (2005). The first adjustment consists in the model with the best reply and inertia introduced in Sect. 2. The second adjustment is proposed in , where agents are assumed to follow a profit-driven heuristic behavior with anchoring attitude. ...
In this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.
... Puu et al. [Puu, 1996[Puu, , 1998Puu & Panchuk, 2009] studied the Cournot duopoly model with elastic demand function and constant marginal cost, and they found that there would appear a strange attractor which has fractal dimension. Bonanno and Zeeman [1985] and Bonanno [1988] found that if each firm has limited knowledge of demand which is linear approximated of their own demand curve, that indeed maximized its profit. Agiza et al. [Agiza et al., 2001;Agiza & Elsadany, 2003, 2004 have studied the complex behaviors of duopoly game in a three oligarch model with nonlinear demand function. ...
This paper examines the optimal decisions of dual-channel game model considering the inputs of retailing service. We analyze how adjustment speed of service inputs affect the system complexity and market performance, and explore the stability of the equilibrium points by parameter basin diagrams. And chaos control is realized by variable feedback method. The numerical simulation shows that complex behavior would trigger the system to become unstable, such as double period bifurcation and chaos. We measure the performances of the model in different periods by analyzing the variation of average profit index. The theoretical results show that the percentage share of the demand and cross-service coefficients have important influence on the stability of the system and its feasible basin of attraction.
... A comprehensive survey of earlier developments is provided by the classical book of Okuguchi [32]. A further stream of literature departed from the assumption of complete knowledge of market demand curve (and therefore of profit functions), and adopted the view that firms are only able to obtain a correct empirical estimate of their marginal profit at the current output levels, thus following a 'gradient' adjustment process 1 [10,19,17,12,8]. Again, existence and stability of the equilibrium was one of the central issues in such studies. ...
This chapter deals with a stylized discrete-time model of a financial market with one risky asset and one risk-free asset, under the interaction of two standard types of investors, fundamentalists and chartists. The model is developed under two alternative market clearing mechanisms, namely, the Walrasian auctioneer and the market maker mechanism. In both cases the price dynamics is described by a two-dimensional nonlinear map, and the two models have the same, unique 'fundamental' steady state. Comparison of the local stability properties of the steady state under the two pricesetting scenarios highlights the analytical conditions under which the steady state is locally stable with one market mechanism, but unstable with the other. Such conditions involve the price adjustment parameter of the market maker, in connection to the slope of the aggregate demand curve in the Walrasian auctioneer setting. Numerical simulation reveals, however, that such local properties may be less important in explaining which of the two mechanisms produces larger price fluctuations, when the steady state is destabilized.
... Let us consider here a dynamic adjustment based on profit gradient (or marginal profits) a decision rule often proposed in the economic literature on boundedly rational agents (see e.g. [3,5,50,16,15,22,42,11,10]) ...
... A solution in between the subjective and the objective approach was firstly developed by Silvestre (1977), who added a hypothesis in order to link subjective and objective demand functions: the slope of the former demand curve coincides with the slope of the latter: firms know the current elasticity. Afterwards this model was recovered by Bonanno and Zeeman (1985) and by Bonanno (1988) at partial equilibrium level in the oligopoly. ...
In this note, we propose a model where a quantity setting monopolist has incomplete knowledge of the demand function. In each period, the firm sets the quantity produced observing only the selling price and the slope of the demand curve at that quantity. Given this information and through a learning process the firm estimates a linear subjective demand curve. We show that the steady states of the dynamic equation are critical points of the objective profit function. Moreover, results depend on convexity/concavity of the demand. When the demand function is convex and the objective profit function has a unique critical point: the steady state is a globally stable maximum; conversely when then steady state is not unique, local maximums are locally stable, while local minimums are locally unstable. On the other hand when the demand function is concave, the unique critical point is a maximum: there can be stability or instability of the critical point and period two cycles around it via a flip bifurcation. Moreover, through simulations we can observe that, with a mixed inverse demand function, there are different dynamic behaviors, from stability to chaos and that we have transition to complex dynamics via a sequence of period-doubling bifurcations. Finally, we show that the same results can be obtained if the monopolist is a price setter.
... 35. Bonanno and Zeeman (1985), unlike Silvestre (1977b), do not require the demand curves to be downward-sloping. The only requirements are that demand becomes zero at some (possibly very large) price and that the market is viable, in the sense that when price. ...
This survey is organized as follows. I. Introduction. II. The main issues. III. Negishi's model. IV. Objective demand in the Cournot-Nash framework. V. Objective demand in the Bertrand-Nash framework. VI. The assumption of quasi-concavity of the profit functions. VII. Compromises between the conjectural and the objective approach. VIII. Insights into the notion of perfect competition. IX. Conclusion.
... This adjustment mechanism, which is sometimes called myopic (see [20,21]) has been recently proposed by many authors, see e.g. [6,14,15,23,40,41] , mainly with continuous time and constant a i . However, fol- lowing [9,12], we believe that a discrete time decision process is more realistic since in real economic systems production decisions cannot be revised at every time instant. ...
A Cournot duopoly game is proposed where the interdependence between the quantity-setting firms is not only related to the selling price, determined by the total production through a given demand function, but also on cost-reduction effects related to the presence of the competitor. Such cost reductions are introduced to model the effects of know-how spillovers, caused by the ability of a firm to take advantage, for free, of the results of competitors' Research and Development (R&D) results, due to the difficulties to protect intellectual properties or to avoid the movements of skilled workers among competing firms. These effects may be particularly important in the modeling of high-tech markets, where costs are mainly related to R&D and workers' training. The results of this paper concern the existence and uniqueness of the Cournot–Nash equilibrium, located at the intersection of non-monotonic reaction curves, and its stability under two different kinds of bounded rationality adjustment mechanisms. The effects of spillovers on the existence of the Nash equilibrium are discussed, as well as their influence on the kind of attractors arising when the Nash equilibrium is unstable. Methods for the global analysis of two-dimensional discrete dynamical systems are used to study the structure of the basins of attraction.
... It is more likely, however, that real firms only use some local estimate of the demand function, obtained through market experiments, when they compute their strategic variables as solutions to a profit maximization problem. Some authors use terms like " estimated " or " perceived " or " subjective " demand function, in order to say that the demand function that the firms use to solve their profit maximization problem is obtained through market experiments or by some " rule of thumb " (Baumol and Quandt, 1964; Silvestre, 1977; Bonanno and Zeeman, 1985). Many authors have recently investigated the possible outcomes of repeated oligopoly games where the players have a misspecified knowledge of the demand function. ...
We propose an oligopoly game where quantity setting firms have incomplete information about the demand function. At each time step they solve a profit maximization problem assuming a linear demand function and ignoring the effects of the competitors’ outputs. Despite such a rough approximation, that we call “Local Monopolistic Approximation” (LMA), the repeated game may converge at a Nash equilibrium of the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. In the case of isoelastic demand, we show that the game based on LMA always converges to a Nash equilibrium. This result, compared with “best reply” dynamics, shows that in this particular case less information implies more stability.
... Unfortunately, the assumption of demand differentiability is essential to firstorder equilibrium. In a partial equilibrium model, Bonanno and Zeeman (1985) show the existence of first-order equilibrium without assuming downward sloping demand curves but the demand differentiability is still assumed. In fact, without demand differentiability, first-order equilibrium may fail to exist. ...
Purely based on normal assumptions on consumer preferences and production technology, the literature has not established the existence of any equilibrium with imperfect competition beyond that of Negishi equilibrium. In a general equilibrium model with intermediate goods, one firm's demand function cannot be determined unless we know its downstream firms' demand functions. Hence even the existence of demand functions becomes problematic. We introduce generalized first-order equilibrium (GFE), where every firm perceives a linear demand curve, whose slope is bounded by the left and right limits of the objective demand derivatives. Given normal consumer preferences and technology, there always exists a GFE in a price setting economy with intermediate goods.
... Assuming that each player chooses his/her strategy variable according to a payoff function defined over the whole set of strategies, a k-LCE is a strategy profile at which players correctly perceive the kth-order Taylor expansion of their payoff function. For example, a first-order locally consistent equilibrium (1-LCE) of a game is a configuration of strategies at which the first-order condition for payoff maximization is simultaneously satisfied for all players (see Silvestre, 1977;Bonanno and Zeeman, 1985;Gary-Bobo, 1989;D'Agata, 1996). 1 The concept of 2-LCE, applied in this paper, is a profile of strategies which makes the first derivative of the payoff function equal to zero and makes the second derivative negative, i.e., it ensures that a set of local maxima is reached in equilibrium (see Bonanno, 1988;D'Agata, 2000). In such an equilibrium, no player faces an incentive to deviate unilaterally from its equilibrium strategy by some small readjustment of his/her strategy variable. ...
While the properties of equilibria in games of interjurisdictional tax competition have been heavily scrutinized, no hard evidence is available that these equilibria exist. Even for the fundamental tax competition game introduced by Zodrow and Mieszkowski [J. Urban Econ. 19 (1986) 356] and Wildasin [J. Public Econ. 35 (1988) 229], only few positive, but arguably restrictive, results have been derived. Applying a weaker concept than the standard Nash equilibrium—the concept of a second-order locally consistent equilibrium (2-LCE)—we are able to show both the existence and uniqueness of a symmetric equilibrium in tax rates, when regions are homogeneous and either (i) there are only two regions, (ii) capital demand curves are concave, (iii) the inverse of the elasticity of the marginal product of capital is not increasing, or firms apply (iv) CES, (v) Cobb–Douglas, or (vi) logistic production functions.
In this paper, delay differential equations are adopted to describe the ordering performance of the risk-averse newsvendor with supply chain financing. Firstly, authors theoretically explore the local asymptotical stability for equilibrium point, and also the conditions and directions for Hopf bifurcation of the ordering quantity for risk-averse retailer. Secondly, they investigate the influence of important parameters on the bifurcation, and find that the initial capital, risk aversion and friction coefficient can make the Hopf bifurcation undergo a long time, but the adjustment speed induces the inverse effect. Then phase diagram, stable region, bifurcation to chaos, time series and CVaR profit are illustrated by means of numerical simulation. It is found that the upstream supplier can share the risk from market uncertain with stochastic demand under supply chain financing. The results also indicate that the optimal ordering quantity placed by risk-averse newsvendor is smaller than the risk-neutral ordering quantity. Furthermore, the less initial capital may cause the CVaR profit to increase steadily or drop sharply, which exhibits complex dynamical behaviour in the presence of the time delay. Finally, the stability and bifurcation analysis of a fractional delay ordering model has also been proposed and studied. It is worth pointing out that in this study authors assume there is only one retailer who is risk-averse. Therefore, it will be more interesting and meaningful to consider the scenario having multiple retailers and to incorporate the upstream supplier’s optimal decision into the dynamical decision model.
In this paper we consider firms that learn about market conditions by estimating the demand function using past market data. We show that learning may lead to suboptimal outcomes even when the estimated demand function perfectly fits the observations used in the regression and firms thus perceive to have learned the demand function correctly.
We consider the Salop model with three firms and two types of consumers that differ in their sensitivity to product differences. Firms do not know the demand structure and they apply least squares learning to learn the demand function. In each period, firms estimate a linear perceived demand function and they play the perceived best response to the previous-period price of the other firms.
This learning rule can lead to three different outcomes: a self-sustaining equilibrium, the Nash equilibrium or an asymmetric learning-equilibrium. In this last equilibrium one firm underestimates the demand for low prices and it attracts consumers with high sensitivity only. This type of equilibrium has not been found in the literature on least squares learning before. Both the Nash equilibrium and the asymmetric learning-equilibrium are locally stable therefore the model has coexisting stable equilibria.
We study a large economy in which firms cannot compute exact solutions to the non-linear equations that characterize the equilibrium price at which they can sell future output. Instead, firms use polynomial expansions to approximate prices. The precision with which they can compute prices is endogenous and depends on the overall level of supply. At the same time, firms' individual supplies, and thus aggregate supply, depend on the precision with which they approximate prices. This interrelation between supply and price forecast induces multiple equilibria, with inefficiently low output, in economies that otherwise have a unique, efficient equilibrium. Moreover, exogenous parameter changes, which would increase output were there no computational frictions, can diminish agents' ability to approximate future prices, and reduce output. Our model therefore accommodates the intuition that interventions, such as unprecedented quantitative easing, can put agents into "uncharted territory".
In the oligopoly e-commerce market, the oligarch retailers sell products through traditional channel, while others through both network and traditional channel in order to obtain greater profits. Instead of discussing classic Bertrand game model, which past studies have done, we considered dual-channel retailer who makes price decision through both in network channel and traditional channel. This paper used the bifurcation theory of dynamical system, considering dual-channel retailer who makes delay decision. We performed a numerical simulation on system with different conditions, and some complex phenomenons occured, such as bifurcation and chaos. The results showed that adopting price delay decision in tradition channel would make the system more stable. While, adopting price delay decision in network channel makes the system less stable. When the market is in chaotic state, the using of delay decision would have an effect on the system stability in either traditional or network channels. The system become stable from chaos and would return to chaotic again with the increasing of weight in past period. Some interesting phenomenons happened when dual-channel retailer adopted delay decision in both channels. The superposition of delay decision would make the system more complex. At last, we measured the system’s performance by using profit index. We analyzed the profits of different oligarchs when the system is in different states. When the system is in chaos, the total profits of the oligarchs are obviously less than that in a stable state. Adopting delay decision is a way to avoid profit loss when system is in chaotic period, but this requires the retailer has rich operational experience. That is because adopting delayed decision may not always enhance the competitive strength of oligarchs.
The book focuses on the dynamics of nonlinear oligopoly models. It discusses the classical Cournot model with a large variety of demand and cost functions that illustrate the many different types of possible best response functions and it shows the existence of unique and multiple equilibria. Particular emphasis is placed on the influence of nonnegativity and capacity constraints. Dynamics are introduced under various assumptions for the adjustment process. An introduction to the analysis of global dynamics is given through some specific examples. The book also considers concave and general oligopolies and gives conditions for the local asymptotic stability of their equilibria, and it investigates global dynamics in some special cases. Other oligopolies examined include market share attraction games, labor-managed oligopolies, partially cooperating firms and models with intertemporal demand attraction. Local/global stability analyses are carried out for these models and the impact of constraints is discussed. The book contains a number of technical appendices that summarize techniques of global dynamics not easily accessible elsewhere. © Springer-Verlag Berlin Heidelberg 2010. All rights are reserved.
Introduction.- Subjective and objective equilibria.- Introduction.- The basic framework.- Perfect foresight and equilibrium concepts.- Learning dynamics.- Summary.- General equilibrium with imperfect competition.- Introduction.- Quantity competition.- Price competition.- Summary.- Intertemporal macroeconomic equilibrium.- Introduction.- Temporary and intertemporal equilibrium.- Indeterminacy of perfect foresight equilibria and involuntary unemployment.- Indeterminacy of rational expectations equilibria.- Summary and discussion.- A dynamic macroeconomic model with price setting firms.- Introduction.- The economy.- A parametric specification.- Analysis of the dynamics.- Summary and discussion.- Final remarks.
For decades the principle mathematical modeling approach to the manufacturing facility location problem has consisted of models which assume fixed demand and fixed prices. These models generally seek to minimize the firm’s costs (or maximize its profits) subject to meeting the predetermined demand constraints. More recently, efforts have begun to incorporate explicitly into mathematical models the impact that new facilities’ production will have on market prices; and therefore, upon the firm’s profit maximizing location decision. Explicit recognition of market forces in these models requires that one formulate the firm’s demand in a price elastic manner. There are a number of techniques for developing locational models which recognize the impact of price elasticity on a firm’s production decisions. One approach to developing such formulations consists of integrating or linking an economic equilibrium model with a fixed demand facility location model to create an equilibrium facility location problem or model. An equilibrium facility location model represents a locational decision-making technique which, in determining optimal location choices, takes into account the interactions between a location decision and market forces.
This paper considers dual-channel game model with bounded rationality, using the theory of bifurcations of dynamical system. The business objectives of retailers are assumed to be different, which is closer to reality than previous studies. We study the local stable region of Nash equilibrium point and find that business objectives can expand the stable region and play an important role in price strategy. One interesting finding is that a fiercer competition tends to stabilize the Nash equilibrium. Simulation shows the complex behavior of two dimensional dynamic system, we find period doubling bifurcation and chaos phenomenon. We measure performances of the model in different period by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of adaptive adjustment mechanism when the model exhibits chaotic behavior and then allows the retailers to eliminate the negative effects.
This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.
A dynamic Cournot duopoly game, characterized byrms with bounded rationality, is represented by a discrete-time dynamical system of the plane. Conditions ensuring the local stability of a Nash equilibrium, under a local (or myopic) adjustment process, are given, and the in°uence of marginal costs and speeds of adjustment of the tworms on stability is studied. The stability loss of the Nash equilibrium, as some parameter of the model is varied, gives rise to more complex (periodic or chaotic) attractors. The main result of this paper is given by the exact determination of the basin of attraction of the locally stable Nash equilibrium (or other more complex bounded attractors around it), and the study of the global bifurcations which change the structure of the basin from a simple to a very complex one, with consequent loss of predictability, as some parameters of the model are allowed to vary. These bifurcations are studied by the use of critical curves, a relatively new and powerful method for the study of noninvertible two-dimensional maps.
For regular oligopolies (both homogeneous and heterogeneous) the (local) Cournot-Nash equilibria are the (non-degenerate) critical points of a Morse-Smale vector field, defined on the feasible region of non-negative prices and outputs. When at the boundary of this feasible region this vector field points inwards, it follows from the Morse inequalities that there is at least one stable equilibrium. When there is a unique, non-stable, interior equilibrium, necessarily the vector field points outwards somewhere along the boundary of the feasible region. This raises to a stable boundary equilibrium.
This paper shows how a market reaches a unique steady state in monopolistic competition. Without knowing anything about strategic interdependence and only perceiving a linear demand for its own product, every firm follows a simple price strategy to maximize its current profit in each period. The strategy is based on a firm’s own cost function, slope estimate, and its sales and price in the previous period. We show that a market with asymmetric and non-linear demand converges to a unique steady state under rather general conditions.
We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas the other adjusts its production according to the gradient of its profit. Although excessive reaction of the latter firm generally results in destabilization of the ‘Cournot–Nash’ equilibrium and brings about complex dynamic scenarios, this occurs via qualitatively different bifurcation routes, depending on the ratio between firms’ marginal costs. The paper also provides a preliminary exploration of the long-run sustainability of the heterogeneous duopoly competition, by investigating numerically the impact of fixed costs on firms’ survival, along different output trajectories.
This paper considers a probabilistic duopoly in which products are described by their specific attributes, this form of differentiation embodying the horizontal and vertical dimensions. Consumers make discrete choices and follow a random decision rule based on these attributes. A three-stage game is studied in which firms develop new attributes for their products (innovation), then may imitate the attributes of the competing product and finally compete in price. At the equilibrium, the firm selling the less appreciated product is generally incited to imitate its rival. Confronted to a threat of imitation, the benchmark firm sometimes decreases strategically its attribute index in order to diminish its unit cost of innovation and the differentiation on the market, deterring the imitation in this way. This strategy is efficient when imitation costs are sufficiently concave. In the opposite case, it is preferable for the benchmark firm to accept the imitation. Thus, according to the shape of imitation costs, equilibria with "deterrence" or with "accommodation" occur, completing the current typology of strategic responses to a threat of imitation.
This paper investigates the existence of oligopoly equilibria when firms arrive, through local price experiments, at a correct estimation of their demand curves in a neighborhood of a given statu s quo. The author provides sufficient conditions for the existence of a local Nash equilibrium, defined as a point where each firm is at a local maximum of its profit function, given the prices charged by th e other firms. He also provides two examples, one of a duopoly with l ocal Nash equilibria but no Nash equilibria and the other of a duopol y with no local Nash equilibria. Copyright 1988 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
We demonstrate how to estimate a model of oligopoly pricing when products are multi-dimensionally differentiated. We provide
an empirical counterpart to recent theoretical work on product differentiation. Using specifications informed by economic
theory, we estimate price-cost margins for products differentiated in many dimensions.
A simple duopoly model is used to show the advantage to a manufacturer of se lling his product through an independent retailer (vertical separatio n) rather than directly to consumers (vertical integration). Vertical separation is profitable insofar as it induces more friendly behavio r from the rival manufacturer. The authors consider the case where fr anchise fees can be used to extract retailers' surplus. They show tha t vertical separation is in the collective, as well as individual, in terest of manufacturers, and hence facilitates some collusion in the simple setting that they examine. Copyright 1988 by Blackwell Publishing Ltd.
A kth-order locally consistent equilibrium (k-LCE) is an imperfectly competitive general equilibrium allocation at which firms perceive only a kth-order Taylor expansion of their true demand curves. It is shown that, under simple regularity conditions, the set of kth-order locally consistent equilibrium strategies coincides with the set of Cournot-Walras equilibria as soon as k ⩾ 1. In addition, a characterization of the set of Negishi equilibria (or 0-LCEs) and an existence result for 1-LCEs in private ownership economies are provided.
This study analyzes the effects of right-wing extremism on the well-being of immigrants based on data from the German Socio-Economic Panel (SOEP) for the years 1984 to 2006 merged with state-level information on election outcomes. The results show that the life satisfaction of immigrants is significantly reduced if right-wing extremism in the native population increases. Moreover ; the life satisfaction of highly educated immigrants is affected more strongly than that of low-skilled immigrants. This supports the view that policies aimed at making immigration more attractive to the high-skilled have to include measures that reduce xenophobic attitudes in the native population. --
This paper provides a survey on studies that analyze the macroeconomic effects of intellectual property rights (IPR). The first part of this paper introduces different patent policy instruments and reviews their effects on R&D and economic growth. This part also discusses the distortionary effects and distributional consequences of IPR protection as well as empirical evidence on the effects of patent rights. Then, the second part considers the international aspects of IPR protection. In summary, this paper draws the following conclusions from the literature. Firstly, different patent policy instruments have different effects on R&D and growth. Secondly, there is empirical evidence supporting a positive relationship between IPR protection and innovation, but the evidence is stronger for developed countries than for developing countries. Thirdly, the optimal level of IPR protection should tradeoff the social benefits of enhanced innovation against the social costs of multiple distortions and income inequality. Finally, in an open economy, achieving the globally optimal level of protection requires an international coordination (rather than the harmonization) of IPR protection.
The design of distribution channels is an important marketing decision since a revision implies costly reorganization. Hence, it makes sense to study strategic motives of alternative distribution devices. A precommitment is a strategic move that affects the other players' expectations on how oneself will behave and thus induces them to choose in one's own favor (Schelling, 1960). How these tactics can be used by firms to favorably influence competition between vertical chains is the topic of the literature reviewed in this survey. Copyright 1998 by Blackwell Publishers Ltd
This study analyzes the effects of right-wing extremism on the well-being of immigrants based on data from the German Socio-Economic Panel (SOEP) for the years 1984 to 2006 merged with state-level information on election outcomes. The results show that the life satisfaction of immigrants is significantly reduced if right-wing extremism in the native population increases. Moreover ; the life satisfaction of highly educated immigrants is affected more strongly than that of low-skilled immigrants. This supports the view that policies aimed at making immigration more attractive to the high-skilled have to include measures that reduce xenophobic attitudes in the native population. --
Existence of local and infinitestimal Nash equilibria in two-person games with applications to duopoly
- Bonanno
G. BONANNO, Existence of local and infinitesimal Nash equilibria in two-person games with applications to duopoly, Working Paper N. 1, Associazione Borsisti Luciano Jona, Turin, December 1983.