Chaos in duopoly pricing

Puu, Tönu

doi:10.1016/0960-0779(91)90045-b

Cited by 362 publications

(245 citation statements)

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“…For more details, see for example Huang et al (2013). Various papers in oligopoly competition consider iso-elastic demand (see, e.g., Lau andLau (2003), Beard (2013) and Puu (1991)). In Puu (1991), the authors study the dynamics of two competing firms in a market in terms of Cournot's duopoly theory.…”

Section: Multiplicative Noisementioning

confidence: 99%

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

2016

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This paper studies government subsidies for green technology adoption while considering the manufacturing industry's response. Government subsidies offered directly to consumers impact the supplier's production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry and consumers) when designing policies. We further show that for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show this is not always the case and the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of under-serving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism.

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Section: Multiplicative Noisementioning

confidence: 99%

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

2016

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“…In fact many authors have shown that such maps may be used to model many economically interesting situations, as clearly stated in [4]. In particular Puu [16] has shown that a very simple duopoly system, with linear costs functions and a hyperbolic demand function, gives rise to a Cournot map with unimodal reaction functions, for which complex behaviors are easily obtained. It is an easy exercise to show that our general results can be usefully applied to the model of Puu, as well as to other economically interesting Cournot maps, like those proposed in [4].…”

Section: Discussionmentioning

confidence: 99%

“…Since the two-dimensional dynamics of T are associated with the properties of a one-dimensional map, in Section 3 such one-dimensional function is studied in detail for the map (5). Although we shall focus our attention on some exemplifying cases, the results, and the methods followed to obtain them, are general and can easily be used to study the dynamical properties of maps of form (2) with arbitrary reaction functions, such as those proposed in [16] or in [17].…”

Section: Introductionmentioning

confidence: 99%

“…1a), but no economic situations are presented that would lead to non-monotonic reaction functions. Simple economic systems whose time evolution can be modeled by a discrete dynamical system of form (2) with unimodal reaction functions have been proposed in [16,10]. In [16] unimodal reaction functions are obtained by assuming a linear cost function and a hyperbolic demand function h 1a .…”

Section: Introductionmentioning

confidence: 99%

“…Simple economic systems whose time evolution can be modeled by a discrete dynamical system of form (2) with unimodal reaction functions have been proposed in [16,10]. In [16] unimodal reaction functions are obtained by assuming a linear cost function and a hyperbolic demand function h 1a . In [10] a di erent microeconomic foundation for the occurrence of unimodal reaction functions is proposed by assuming a linear demand function and a nonlinear cost function, so that both the reaction functions assume the form of standard logistic maps, and the Cournot map (2) becomes xY y l 1 y 1 À y Y l 2 x 1 À x 5 with parameters l 1 b 0Y l 2 b 0X In [10] the local stability of the ®xed points in the symmetric case of identical producers, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multistability and cyclic attractors in duopoly games

Bischi

Mammana

Gardini

2000

Chaos, Solitons & Fractals

132

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A dynamic Cournot duopoly game, whose time evolution is modeled by the iteration of a map X xY y 3 r 1 y Y r 2 x , is considered. Results on the existence of cycles and more complex attractors are given, based on the study of the one-dimensional map p x r 1 r 2 x . The property of multistability, i.e. the existence of many coexisting attractors (that may be cycles or cyclic chaotic sets), is proved to be a characteristic property of such games. The problem of the delimitation of the attractors and of their basins is studied. These general results are applied to the study of a particular duopoly game, proposed in M. Kopel [Chaos, Solitons & Fractals, 7 (12) (1996) 2031±2048] as a model of an economic system, in which the reaction functions r 1 and r 2 are logistic maps. Ó

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Complex Oligopoly Dynamics

Puu

Nonlinear Dynamical Systems in Economics

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The probably simplest conditions under which the Cournot duopoly model results in complex dynamics, are isoelastic demand and constant marginal costs. One advantage of this combination is that it is possible to solve for the reaction functions in simple closed form. The model is also studied in an adaptive format, in which case the flip bifurcation of the Cournot equilibrium, leading to a period-doubling cascade to chaos, is replaced by a subcritical Neimark bifurcation. The structure of the Arnol'd periodicity tongues, as well as the chaotic areas in parameter space are studied, as is multistability of attractors.

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Chaos in duopoly pricing

Cited by 362 publications

References 1 publication

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

Multistability and cyclic attractors in duopoly games

Complex Oligopoly Dynamics

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