On the Markovian efficiency of Bertrand and Cournot equilibria

Colombo, Luca; Labrecciosa, Paola

doi:10.1016/j.jet.2014.11.007

Cited by 38 publications

(18 citation statements)

References 43 publications

(102 reference statements)

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“…That is, since the game is a linear state one by construction, one of the linear feedback strategies generated by the HJB equation degenerate in the open-loop one, coinciding with the static Cournot-Nash solution. 5 The expression on the r.h.s. of (17) …”

Section: The Linear Feedback Solutionmentioning

confidence: 99%

Regulating the Tragedy of Commons: Nonlinear Feedback Solutions of a Differential Game with a Dual Interpretation

Lambertini

2017

SSRN Journal

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A well established dynamic model describing the impact of oligopolistic interaction on a renewable resource is revisited here to illustrate its dual interpretation as a waste removal differential game. The regulatory implications are illustrated by assuming that the public agency may control market price and possibly also access to the commons. Two different formulations of the managerial or CSR objective are envisaged, based on a combination of profits and either output or the individual share of the waste stock. It is shown that if the representative firm's objective includes the residual waste stock, there exists a unique regulated price driving to zero the steady state stock itself.Hence, the present analysis delivers some useful indications concerning an appropriate definition of the CSR objective firms should adopt.JEL Codes: C73, L13, Q20, Q53

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Section: The Linear Feedback Solutionmentioning

confidence: 99%

Regulating the Tragedy of Commons: Nonlinear Feedback Solutions of a Differential Game with a Dual Interpretation

Lambertini

2017

SSRN Journal

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“…The assumption that the resource conversion rate in the output is 1:1 is equivalent, as observed by Colombo and Labrecciosa (2015), to the hypothesis that the transformation of the resource happens using capital, labor and other inputs (which remain in the background of the model), where each quantity is a multiplicative factor in the production function, normalized to 1 without loss of generality. The resource stock dynamic is given by the following differential equation:…”

Section: The Modelmentioning

confidence: 99%

“…Fujiwara (2011) proposes an asymmetric oligopoly model with linear feedback strategies, in which efficient and non-efficient (with nonzero marginal costs) firms compete. Differentiated products and imperfect product substitutability have been introduced in a symmetric duopoly model by Colombo and Labrecciosa (2015), in order to deal also with price competition à la Bertrand, and they provide also a complete investigation of nonlinear feedback strategies.…”

Section: Introductionmentioning

confidence: 99%

A differential game in a duopoly with instantaneous incentives

Grilli

Bisceglia

2017

Decisions Econ Finan

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In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.Mathematics Subject Classification 91A23 · 49N90 · 91A80 · 91B76 · 91A10 JEL Classification C61 · C72 · C73 · D21 · D23 · D43 · D60 · H23 · Q20

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“…To characterise the continuum of nonlinear feedback solutions, we adopt the same procedure as in Rowat (2007), 4 again con…ning to symmetric equilibria.…”

Section: Nonlinear Feedback Equilibriamentioning

confidence: 99%

“…The setup is the same as in Benchekroun (2003), Fujiwara (2008) and Colombo and Labrecciosa (2015). The model illustrates a di¤erential oligopoly game of resource extraction unravelling over continuous time t 2 [0; 1) : The market is supplied by two fully symmetric …rms 2 producing a homogeneous good, whose inverse demand function is p = a X at any time t, with…”

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On the (In)Stability of Nonlinear Feedback Solutions in a Dynamic Duopoly with Renewable Resource Exploitation

Lambertini

Mantovani

2016

SSRN Journal

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We revisit Fujiwara's (2008) di¤erential duopoly game to show that the degenerate nonlinear feedback identi…ed by the tangency point with the stationary state line is indeed unstable, given the dynamics of the natural resource exploited by …rms. To do so, we fully characterise the continuum of nonlinear feedback solution via Rowat's (2007) method, characterising the in…nitely many stable nonlinear feedback equilibria.JEL codes: C73, L13, Q2

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On the Markovian efficiency of Bertrand and Cournot equilibria

Cited by 38 publications

References 43 publications

Regulating the Tragedy of Commons: Nonlinear Feedback Solutions of a Differential Game with a Dual Interpretation

Regulating the Tragedy of Commons: Nonlinear Feedback Solutions of a Differential Game with a Dual Interpretation

A differential game in a duopoly with instantaneous incentives

On the (In)Stability of Nonlinear Feedback Solutions in a Dynamic Duopoly with Renewable Resource Exploitation

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