Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics

Frutos, Javier de; Martín‐Herrán, Guiomar

doi:10.1007/s10957-014-0573-z

Cited by 16 publications

(6 citation statements)

References 32 publications

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“…The constant term X i in (A.2) has the expression in (19). The stationary equilibrium of the dynamics (13), (14) subject to (15) is globally asymptotically stable because the matrix system B − D is negative definite if at least one of the d i , i = 1, .…”

Section: Proof Of Propositionmentioning

confidence: 99%

Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

Frutos

Martín‐Herrán

2019

European Journal of Operational Research

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We analyze a transboundary pollution differential game where, in addition to the standard temporal dimension, a spatial dimension is introduced to capture the geographical relationships among regions. Each region behaves strategically and maximizes its welfare net of environmental damage caused by the pollutant stock. The emission-output ratio is reduced by investment in region specific clean technology which evolves over time. The spatio-temporal dynamics of the pollutant stock is described by a parabolic partial differential equation. Using aggregate variables we study the feedback Nash equilibrium of a discrete-space model which could be seen as a space discretization of the continuous-space model. The discrete-space model presents the three main features of the original formulation: the model is truly dynamic; the agents behave strategically; and the model incorporates spatial aspects. For special functional forms previously used in the literature we analytically characterize the feedback Nash equilibrium and evaluate the impact of the introduction of the spatial dimension in the economic-environmental model. We show that our spatial model is a generalization of the model that disregards the spatial aspects. We analytically show that as the parameter describing how pollution diffuses among regions tends to infinity the equilibrium policies converge to those in the non-spatial setting. In the non-cooperative framework the spatially non-myopic behavior prescribes lower equilibrium emission rates, and consequently a lower global pollution stock. This is compatible with greater long-run welfares. In the cooperative framework, although the strategic interaction among the players does not exist, the only decision-maker still makes spatially strategic decisions.

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Section: Proof Of Propositionmentioning

confidence: 99%

Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

Frutos

Martín‐Herrán

2019

European Journal of Operational Research

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“…The approximation is constructed solving the Bellman equation for the discrete-time model. The approach has been previously used, in the context of differential games, in [10], [12].…”

Section: Introductionmentioning

confidence: 99%

On Discrete-Time Approximations to Infinite Horizon Differential Games

Frutos¹,

Gatón²,

Novo³

2021

Preprint

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In this paper we study a discrete-time semidiscretization of an infinite time horizon noncooperative N -player differential game. We prove that as the discretization time step approaches zero the discrete-time value function approximate the value function of the differential game. Furthermore, the discrete-time Nash equilibrium is an ǫ-Nash equilibrium for the continuous-time differential game. * Research supported by Spanish MCI under grants PID2019-104141GB-100 (AEI) (AEI/FEDER, UE) and VA169P20 (Junta de Castilla y Leon, ES) co-financed by FEDER funds (EU).

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“…Furthermore, incentive strategies that establish the efficient solution as an incentive equilibrium have been developed (see, e.g., [13]). And, more recently, also nonlinear incentive strategies have been proposed by [12] which are credible in a large region of the cooperative trajectory.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of an uncertain simple fishery management game

Engwerda

2018

Fisheries Research

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This note analyzes in a fishery management problem the effects of relaxing one of the usual assumptions in the literature of dynamic games. Specifically, the assumption that players restrict to strategies that stabilize the system. Previous works in the literature have shown that feedback Nash equilibria can exist in which a player can improve unilaterally by choosing a feedback control for which the closed-loop system is unstable. This paper considers in some more detail the implication this setting has in the framework of a simple fishery management. It is shown that if the fishermen are not short-sighted in their valuation of future profits, the considered approach implies a division of them into two groups. One group going for maximal profits and the other group taking care of the imposed stability constraint.To see how noise might impact these results we additionally consider a framework where fishermen take into account the possibility that the fish growth might be corrupted by external factors. We consider a deterministic approach of dealing with noise in this set-up.The model predicts that the more people are involved in the group taking care of the stabilization constraint, the less active they get. Furthermore it predicts that the natural reaction of any of these persons is to increase his activities if he expects more noise. But that this activity is reduced, and partly replaced by more active control policies by group members, if the size of the group increases. Activity of fishermen going for maximal profits is not affected by noise expectations.

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Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics

Cited by 16 publications

References 32 publications

Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

On Discrete-Time Approximations to Infinite Horizon Differential Games

Stabilization of an uncertain simple fishery management game

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