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Noncooperative Resource Exploitation by Patient Players

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Abstract

We consider a discrete-time dynamic game in which a finite number of players extract a non-renewable resource and derive consumption solely from the extracted amount (cake-eating game). Markov perfect Nash equilibria consisting of linear strategies can be constructed in this game not only if the players have time-preference factors that are smaller than 1, but also if these factors are equal to or even larger than 1. We demonstrate this result both for the case of identical players and for the case of heterogeneous players. In addition, we study the influence of the model parameters on the equilibrium.

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Notes

  1. Note that we define the property of being a MPNE only for feasible strategy profiles, i.e., for profiles satisfying condition (3). Sundaram [10] uses an ad hoc rule to determine the consumption rates for infeasible strategy profiles. The important point is that there is no way to place conditions on the primitives of the model that guarantee that a strategy profile will always be feasible.

  2. Later in this section, we shall discuss the model without discounting.

  3. For the parameter set \((\alpha _1,\alpha _2,\rho _1,\rho _2)=(2/3,1/4,1.05,1.05)\) there does not exist a MPNE consisting of linear strategies.

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Acknowledgments

The authors are grateful for the detailed and constructive comments of an anonymous referee.

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Authors and Affiliations

  1. Department of Economics, Cornell University, Ithaca, NY, 14853, USA

    Tapan Mitra

  2. Department of Economics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Gerhard Sorger

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  1. Tapan Mitra
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  2. Gerhard Sorger
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Correspondence to Gerhard Sorger.

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Mitra, T., Sorger, G. Noncooperative Resource Exploitation by Patient Players. Dyn Games Appl 5, 361–377 (2015). https://doi.org/10.1007/s13235-015-0135-5

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