Groundwater extraction among overlapping generations: a differential game approach

Groundwater is a common resource that has been wasted for years. Today, we pay the consequences of such inappropriate exploitation and we are aware that it is necessary to realize policies in order to guarantee the use of this resource for future generations. In fact, the irrational exploitation of water by agents, nevertheless it is a renewable resource, may cause its exhaustion. In our paper, we develop a differential game to determine the efficient extraction of groundwater resource among overlapping generations. We consider intragenerational as well as intergenerational competition between extractors that exploit the resource in different time intervals, and so the horizons of the players in the game are asynchronous. Feedback equilibria have been computed in order to determine the optimal extraction rate of “young” and “old” agents that coexist in the economy. The effects of the withdrawal by several generations are numerically and graphically analyzed in order to obtain results on the efficiency of the groundwater resource.

[1]  Encarna Esteban,et al.  Groundwater and ecosystems damages: Questioning the Gisser–Sánchez effect , 2011 .

[2]  R. Banker.  A game theoretic approach to measuring efficiency , 1980 .

[3]  David W. K. Yeung,et al.  Inter‐ and intragenerational renewableresource extraction , 1999, Ann. Oper. Res..

[4]  Lucia Maddalena,et al.  GROUNDWATER MANAGEMENT AND AGRICULTURE , 2018 .

[5]  Veijo Kaitala,et al.  Equilibria in a stochastic resource management game under imperfect information , 1993 .

[6]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[7]  A. Charnes,et al.  Constrained game formulations and interpretations for data envelopment analysis , 1989 .

[8]  Bill Provencher,et al.  The Externalities Associated with the Common Property Exploitation of Groundwater , 1993 .

[9]  Alex Mourmouras,et al.  Conservationist government policies and intergenerational equity in an overlapping generations model with renewable resources , 1993 .

[10]  Phoebe Koundouri,et al.  Current Issues in the Economics of Groundwater Resource Management , 2004 .

[11]  Lucia Maddalena,et al.  Competition and cooperation in the exploitation of the groundwater resource , 2018, Decisions in Economics and Finance.

[12]  Luca Grilli,et al.  Resource extraction activity: an intergenerational approach , 2003 .

[13]  Peter Burton,et al.  Intertemporal Preferences and Intergenerational Equity Considerations in Optimal Resource Harvesting , 1993 .

[14]  M. Morán,et al.  General dynamics in overlapping generations models , 1995 .

[15]  Simone Clemhout,et al.  Dynamic common property resources and environmental problems , 1985 .

[16]  Carl Chiarella,et al.  On the Economics of International Fisheries , 1984 .

[17]  M. Gisser,et al.  Competition versus optimal control in groundwater pumping , 1980 .

[18]  Donald H. Negri.  The common property aquifer as a differential game , 1989 .

[19]  S. Jørgensen,et al.  Stochastic differential game model of a common property fishery , 1996 .

[20]  Santiago J. Rubio,et al.  Strategic Behavior and Efficiency in the Common Property Extraction of Groundwater , 2003 .

[21]  Santiago J. Rubio,et al.  Competitive versus efficient extraction of a common property resource: The groundwater case , 2001 .