Extraction of non-renewable resources: a differential game approach

Halkos, George and Papageorgiou, George (2008): Extraction of non-renewable resources: a differential game approach. Published in: Archieves of Economic History , Vol. 1, No. XXI (2008): pp. 5-22.

Abstract

Exploitation of non–renewable resources is an intensively studied field of environmental economics in the last century. Since the influential Hotelling’s paper a huge progress is made in the depletable resources literature. Although a variety of methodologies is used in that problem’s solutions a basic question of time inconsistency arises in the solution process. We show the sources of dynamical time inconsistency in a leader – follower game for which the buyer leads while the extractor follows and the players employ open loop strategies. Also we make use of Markovian informational structure, in a non – renewable resource Nash game, in order to extract strategies that are time consistent. Finally we enlarge the utility function space from the logarithmic utility to the utility functions that exhibits relative risk aversion with the same, with respect to time consistency, strategies.

• Item Type: MPRA Paper
• Language: English
• Keywords: Non-renewable resources; time consistency; Markovian strategies; leader-follower
• Subjects: Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q0 - General > Q00 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q30 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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