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Aggregative Environmental Games

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Abstract

This paper expounds a new approach to the analysis of public good and open access resource models, developed in a series of recent papers by Cornes and Hartley, and considers the applicability of this approach to modeling current environmental problems. I look at a number of possible extensions of the framework, survey recent applications to environmental problems, and suggest further possible lines of enquiry.

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Notes

  1. The exposition of this model draws on Cornes and Hartley (2007a), which provides a fuller and more rigorous account.

  2. The rationale for this name is as follows: Given any observable value of the aggregate, Q, there is a uniquely determined quantity—say Z—that can be subtracted from Q such that player i’s best response to \((Q-Z)\) is precisely the quantity Z. In other words, player i’s best response exactly replaces the quantity Z.

  3. We are assuming that the transfer, and therefore the shift in player j’s graph, is not large enough to violate the individual nonnegativity constraint on \({\widehat{q}}_j\).

  4. See also Cornes and Sandler (1994) for further development of this model.

  5. By putting \(\pi _{x} = 1\) throughout, we are adopting characteristic x as the numeraire, in terms of which quantities are being measured in the virtual price regime.

  6. This paragraph is a—possibly too cryptic—summary of the analysis of Cornes and Sandler (1994).

  7. The existing literature nearly always assumes that each player’s contribution to the public good must be nonnegative—she cannot take actions that deplete its level. Cornes and Rübbelke (2012) develop a model that permits some players to like a public quantity, and take actions that augment it, while others dislike it and take actions that reduce it.

  8. Cornes and Hartley (2007a) provide a more detailed discussion of these issues.

  9. The assumption that \(z_{ij}=x_{ij}+y_{ij}\) implies that the two goods that appear in the equations of the model are perfect substitutes. They can therefore be aggregated into a single good, thereby reducing the number of arguments in the typical utility function from 3 to 2.

  10. It may be objected that we risk committing the cardinal sin of dividing by zero. However, as Cornes and Hartley (2000) show, this apparent difficulty is easily dealt with in an intellectually respectable manner.

  11. A more formal discussion and demonstration of these claims can be found in Cornes and Hartley (2000).

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  1. Research School of Economics, Australian National University, Canberra, ACT, 0200, Australia

    Richard Cornes

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  1. Richard Cornes
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Correspondence to Richard Cornes.

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Cornes, R. Aggregative Environmental Games. Environ Resource Econ 63, 339–365 (2016). https://doi.org/10.1007/s10640-015-9900-6

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