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Oligopoly Equilibria When Firms Have Local Knowledge of Demand
Abstract
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.
... However, to the best of our knowledge, only these two existing studies examine the effect of sabotage on team contests, and their focus is on sabotaging members of rival teams rather than teammates. 4 Given the practical and theoretical importance of analyzing intra-team sabotage, we use Nitzan's 1 Readers can find real-world evidence of sabotaging colleagues in Endnote 4 of Murphy (1992). This endnote presents anecdotal evidence, reported by John Dvorak, PC Magazine editor, about how his friend was promoted. ...
... For example, when a company launches a new product, several advertising firms propose methods for sales promotion, and one advertising firm wins the order. 4 The intra-team sabotage might be similar to sabotaging oneself (Gürtler and Münster, 2013); self-sabotage decreases a player's winning probability. Intra-team sabotage by players reduces the winning probability of their teams. ...
... Generally, (4) shows that the "no sabotage" strategy is unlikely to be the best response of a player as gets large. By Proposition 2, (1− )( −1) * decreases in , which implies that the condition in (4) is more likely to be satisfied as increases. ...
This study examines a rent-seeking contest among teams in which members can sabotage their teammates.We demonstrate how rent dissipation differs, with and without intra-team sabotage options. We find that an increased number of teams always increases rent dissipation, with and without sabotage options. In contrast, rent dissipation nonmonotonically changes with the number of team members. These changes in rent dissipation may contribute to alleviating efficiency losses in real-world contests.
... As is pointed out by Roberts and Sonnenschein (1977), lack of quasiconcavity of the proÞt functions may cause the reaction curves to exhibit discontinuities, possibly leading to nonexistence of the Bertrand-Nash equilibrium (nonpathological 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). ...
... librium always exists . However, (1) allows for the situation where some producer is at a local minimum of his proÞt function, since Þrms disregard second order conditions. Note that, if Þrms think they face a linear demand curve, they will believe they are at the global maximum of their proÞt function whenever the Þrst order condition is satisÞed. Bonanno (1988) deÞnes a local Bertrand-Nash equilibrium as a price vector p * = (p * 1 , . . . , p * n ) for which, besides (1) the second order condition for a local maximum is satisÞed, that is, ...
... Hence, instability of the equilibrium is more likely to occur when perceptions of Þrms are less palatable. As a last remark notice that if p * is locally stable in our learning model then it satisÞes the second order conditions for a local Bertrand-Nash equilibrium (compare Bonanno, 1988). That this is the case can be seen by rewriting the Þrst and second order conditions for a maximum as ...
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.
... 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.
... We investigate the equilibrium only in case I. 4 In particular, we have computed the optimal values of x t , y t , X and Y by Corollary 3, for some values of c, s t and r t , and then we have tested whether …rm B has an incentive to deviate from the equilibrium providing a larger or a smaller capacity. For each capacity choice of B, we have …nd the optimal allocation for A and B. The result is obtained by modifying the capacity Y from 0 to the double of the Cournot solution, and then computing the equilibrium using (9). ...
... The explanation is quite simple. See, Equation (9). When capacities of both …rms in the same market are large (Region D), then …rms behave as in a Bertrand game, so that they realize zero pro…ts. ...
This paper provides a simple model of pricing (and capacity choice) for highly per-ishable goods, assuming that installing capacity is costly and high-valuation consumers arrive late. We show that oligopolistic …rms …nd it optimal to engage in intertemporal price discrimination even if there is no uncertainty concerning the arrivals and there is no product di¤erentiation. Indeed, …rms are interested to sell a share of their pro-duction to low-valuation consumers at low prices to reduce their capacity in order to be able to charge high prices to high-valuation consumers. The outcomes of the model suitably describe the pricing behaviour observed in the airline industry. JEL classi…cation: L93; D43; D21.
... Yet, the large country still retains a larger number of firms than the small one: n m 1 > n m 2 . Indeed, as there is no capital price effect in equilibrium, (7) and the equalization of profits between countries implies that the labor-market pooling effect generated by the large country must be exactly offset by a stronger labor crowding effect. This, in turn, means that the large country hosts a larger number of firms. ...
... A similar approach has been proposed byBonanno (1988) in oligopoly theory. ...
This paper develops a two-country model having imperfect matching between firms and workers, and investigates the effects of capital mobility and tax competition, via skill mismatch, on the spatial distribution of firms. Analysis shows that the difference in population between countries matters for the distribution of firms and for the consumers' welfare.
... It is our belief that this concept is empirically relevant because of the difficulty that many decision makers face in accounting for all possible actions. 4 We then identify a condition under which this candidate equilibrium is indeed a Nash equilibrium. ...
... 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.
... One example is the selection introduced by Roberts (1980), which picks the exchange equilibrium closest to a reference point. This selection naturally leads to the equilibrium concept of Bonanno (1988), in which firms have only local knowledge of the market demand function. The following definition of equilibrium is more general, and permits the full variety of price selections. ...
In oligopoly models with differentiated products, producers face a market demand function that reflects the preferences of consumers. However, typical assumptions on preferences place only weak restrictions on the shape of aggregate demand. This may result in profit functions that are not strictly quasiconcave, in best-reply correspondences that are not differentiable, and in equilibria that are not robust to perturbations. This paper establishes differentiability and robustness as a generic property: for an open, dense set of economies, best replies are differentiable in a neighborhood of equilibria, which is a precondition for comparative statics. All these economies have a finite number of equilibria in pure strategies.
... One example is the selection introduced by Roberts (1980), which picks the exchange equilibrium closest to a reference point. This selection naturally leads to the equilibrium concept of Bonanno (1988), in which firms have only local knowledge of the market demand function. The following definition of equilibrium is more general, and permits the full variety of price selections. ...
In oligopoly models with differentiated products, producers face a market demand function that reflects the preferences of consumers. However, typical assumptions on preferences place only weak restrictions on the shape of aggregate demand. This may result in profit functions that are not strictly quasiconcave, in best-reply correspondences that are not differentiable, and in equilibria that are not robust to perturbations. This paper establishes differentiability and robustness as a generic property: for an open, dense set of economies, best replies are differentiable in a neighborhood of equilibria, which is a precondition for comparative statics. All these economies have a finite number of equilibria in pure strategies.
... 4 It may be mentioned here that Bamon and Fraysee (1985) has a related result. 5 Costs are required to be. lower semi-continuous. ...
... 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.
... As mentioned in the Introduction, this concept of "equilibrium" is closely related to that of a second-order Locally Consistent Equilibrium (2-LCE), as introduced by Gary- Bobo (1989) in the context of an imperfectly general equilibrium model, or to the equivalent concept of a Local Nash Equilibrium (LNE) used by Bonanno (1988) in a static oligopoly game. 16 The justification is that firms have only local knowledge of their demand curves (and therefore of their profit functions), so that they experiment through small variations of their strategy variable and stop when they reach a local maximum. ...
This paper provides a political economy analysis of (de)centralization when local public goods—with spillovers effects—can be substitutes or complements. Depending on the degree of complementarity between local public goods, median voters strategically delegate policy to either ‘conservative’ or to ‘liberal’ representatives under decentralized decision-making. In the first case, it accentuates the free-rider problem in public good provision, while it mitigates it in the second case. Under centralized decision-making, the process of strategic delegation results in either too low or too much public spending, with the outcome crucially depending on the sharing of the costs of local public spending relative to the size of the spillover effects. Hence, with a common financing rule, centralization is welfare improving if and only if both public good externalities and the degree of complementarity between local public goods are both relatively large.
... If it happens that (pt+I yt+1) _ (pt, yt),then (pt+I yt+I) is the profit maximizing strategy in F (pt , yt), hence the monopolist will stop the process. Therefore, the following definition is now obvious: A local monopolistic equilibrium (LME) is a strategy (p*, y*) which satisfies the following conditions: (i) (p*, y*) E Ey; (il) p* • y* > p • y for every (p, y) E F(p*, y*) (For an equilibrium concept similar to this, but within a game-theoretic context, see Bonanno (1988)). ...
A general equilibrium model with monopoly is developed in which the mo-nopolist has only local knowledge of the equilibrium manifold and behaves adaptively. We provide sufficient conditions ensuring that the iterative process activated by the mo-nopolist converges to an equilibrium.
... However, due to the analytic intractability of the second stage pricing game when productivities are asymmetric, we cannot guarantee that it remains an equilibrium away from the steady-state, or for other possible calibrations. However, SPLNE's are independently plausible since they only require firms to know the demand curve they face in the local vicinity of an equilibrium, which reduces the riskiness of the experimentation they must perform to find this demand curve (Bonanno 1988). It is arguable that the coordination required to sustain asymmetric equilibria and the computational demands of mixed strategy equilibria render either of these less plausible than our SPLNE. ...
This paper builds a dynamic stochastic general equilibrium (DSGE) model of endogenous growth that generates large medium-frequency cycles while robustly matching the near trend-stationary path of observed output. This requires a model in which standard business cycle shocks lead to highly persistent movements around trend, without significantly altering the trend itself. The robustness of the trend also requires that we eliminate the scale effects and knife edge assumptions that plague most growth models. In our model, when products go out of patent protection, the rush of entry into their production destroys incentives for process improvements. Consequently, old production processes are enshrined in industries producing non-protected products, and shocks that affect invention rates change the proportion of industries with advanced technologies. In an estimated version of our model, a financial-type shock to the stock of ideas emerges as the key driver of the medium frequency cycle.
... 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]) ...
... They argued that learning and pseudo-maximizing rules permitted close approximation of the maximizing price. Bonanno et al. [12] [13] found that if each firm's knowledge of demand was limited to the linear approximation of their own demand curve, they would believe that they had indeed maximizing its profits. Furth [14] and Flam [15] studied the adjustment mechanism which based on the assumption that firms do not have a global knowledge of the demand function, but each of them was able to obtain a correct local estimate of the marginal profit and, in each time period, revised their production according to this profit signal. ...
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.
... The literature dealing with Cournot models has increased greatly in the last two decades. The existence and stability of Cournot equilibria have been analyzed by Furth (1986), via a cubic marginal costs curve, Bonanno (1988), via a cubic marginal revenues curve, and local/global stability properties have become important issues. ...
This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border-collision bifurcations and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real profits.
... 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.
... 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.
... Palander 1939, Theocharis 1960, Fisher 1961, McManus and Quandt 1961) or not unique (Robinson 1933, Palander 1936,1939). The literature dealing with Cournot models has increased greatly in the last two decades: The existence and stability of Cournot equilibria have been analyzed by Furth (1986), via a cubic marginal costs curve, Bonanno (1988), via a cubic marginal revenues curve, and local/global stability properties became important issues. A rich literature stream on this subject is related to duopoly or triopoly models, usually described by continuous and smooth reaction functions (see e.g. ...
This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border-collision bifurcations and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real profits.
... and 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. Bonanno (1988) provides a duopoly example consistent with standard utility maximization, which does not possess either Nash or local maximum equilibrium. At the only possible location for first-order equilibrium, one firm's demand curve is not differentiable 2 . Hence no first- 1 Caplin and Nalebuff (1991) obtain an Bertrand equilibrium with strong co ...
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.
... The instability was shown for a discrete Cournot tâtonnement process. In [11] and [3], as far as I know, for the …rst time in English, the possibility of multiple equilibria was mentioned. 2 In [11] it was shown that the questions about 'uniqueness' and 'stability'are related to each other. ...
Corchón and Mas-Colell [1996. On the stability of best reply and gradient systems with applications to imperfectly competitive models. Economics Letters 51, 59-65] showed that in heterogeneous oligopoly (almost) everything is possible. In order to obtain a similar result for homogeneous oligopoly, either one needs an externality in the cost function, or the reaction correspondences should fulfill a special condition.
... 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.
... The instability was shown for a discrete Cournot tâtonnement process. In [11] and [3], as far as I know, for the …rst time in English, the possibility of multiple equilibria was mentioned. 2 In [11] it was shown that the questions about 'uniqueness' and 'stability'are related to each other. ...
Corchon and Mas-Colell (1996) showed that in heterogeneous (almost) everything is possible. Here it is shown that in order to obtain a similar result for homogeneous oligopoly, the reaction correspondences should fulfill a special condition.
Résumé
La problématique de l'équilibre général en présence de concurrence imparfaite est examinée à l'occasion d'une vue d'ensemble de la littérature consacrée au sujet. On tâchera de souligner à la fois les apports et les limites de la théorie sur cette question, plus particulièrement dans la perspective d'aboutir à des « fondements microéconomiques de la macroéconomie » reposant de façon explicite sur les comportements imparfaitement concurrentiels des agents économiques.
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.
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.
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 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.
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 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.
This note shows the existence of a second-order locally consistent equilibrium in the game analysed in 1988 by Bonanno, under assumptions which are weaker and empirically more satisfactory than usual. An example of application to oligopoly theory is also provided. Copyright 2000 by Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research
We characterise, for both separate and interdependent markets, the local pure-strategies Nash equilibrium of a spatial duopoly game, where consumers are horizontally and vertically heterogeneous, and firms have different cost structures and ranges of product lines. We show that standard results which emerged in the monopoly context can not be generalised to strategic contexts where firms retain market power and there is sufficient competitive pressure. We prove that in the asymmetric duopoly case, when markets are interdependent, the incentive compatibility constraints are slack, and there is no quality distortion. Copyright 2007 The Author
Journal compilation 2007 Blackwell Publishing Ltd/University of Adelaide and Flinders University .
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. --
The oligopoly theory usually refers to the partial equilibrium study of markets in which the demand side is competitive, while the supply side is neither monopolized nor competitive. It is exclusively concerned with single period models. The two models that are mainly discussed are Cournot's and a model based on Chamberlin. In Cournot's model, it is assumed that the products of the firms are perfect substitutes and each firm decides the output levels with price being determined in the market. The Chamberlinian model allows for imperfect substitutability among the outputs of the firms, and each firm is assumed to name prices for their products. The chapter also presents some of the basic structure for the models of multi-period oligopoly. The time structure of none of these models is explicit; however, none of them makes sense when interpreted as strictly single-period models. Thus, for the best understanding of them, it is necessary to augment them by making the time relations explicit and by making an appropriate reformulation of the firm's objective functions. The chapter also examines various models in which the time structure is explicit and the firms seek to maximize discounted profit streams. The chapter also discusses models with entry and exit of firms.
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 paper develops a model of “large group” Chamberlinian monopolistic competition in which (1) there are many firms producing
differentiated commodities, (2) each firm is negligible in that it can ignore its impact on, and hence reactions from, other
firms; (3) free entry leads to zero profit of operating firms; but (4) each firm faces a downward-sloping demand curve. The
existence of a monopolistically competitive equilibrium is established. In a companion paper, more particular questions such
as whether the market provides too many or too few products are addressed for a special case of the model.
Topics in Oligopoly: Local Equilibria, Choice of Product Quality, Entry Deterrence
- G Bonanno
BONANNO, G., "Topics in Oligopoly: Local Equilibria, Choice of Product Quality, Entry Deterrence," Ph.D. thesis, London School of Economics (May 1985).
Dynamic Price and Quantity Setting by a Monopolist Facing Unknown Demand
- P Aghion
- P Bolton
- And B Jullien
AGHION, P., P. BOLTON, AND B. JULLIEN, "Dynamic Price and Quantity Setting by a Monopolist Facing Unknown Demand," mimeo, University of California, Berkeley (November 1986).