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Option Fund Market Dynamics for Threshold Public Goods

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Abstract

Economic agents have the possibility to fund the protection of environmental public goods, such as natural ecosystems and biodiversity, facing unknown risks of collapse, which could help to back them up. On the base of the prediction markets, which meet with a degree of success since their introduction, we propose an evolutionary model of an option fund market for the threshold environmental public goods. We consider population dynamics of agents distributed into proportional fair-share contributors and free riders. The model outcomes show that the public goods could be provided when the agents exchanging option contracts are equally divided into buyers and sellers. This result only holds for a specific social belief over the probability of the public good safeguard, the strict equality between bids and asks, and the equality of all payoffs. Otherwise, providing public goods through option markets turns out to be inoperative.

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Notes

  1. We ignore the case of \(\gamma (1-p)\) on purpose. Indeed, contrary to \(\gamma \) and q, the probability p of species safeguard depends on whether the agent decides to contribute to the public good. This bet is under her control.

  2. Indeed, both the option value and the risk of payoff loss preexist to the market funding.

  3. From the Binomial sampling, we have \(\sum _{m=0}^{M-1} (m+1)^{-1}\left( {\begin{array}{c} M-1 \\ m \\ \end{array}} \right) z^{m}(1-z)^{M-1-m}\)  \(=\sum _{m=1}^{M-1} M^{-1}\left( {\begin{array}{c} M \\ m+1 \\ \end{array}} \right) z^{m}(1-z)^{M-1-m}\) \(=(Mz)^{-1}\left[ {\sum _{m=0}^M \left( {\begin{array}{c} M \\ m \\ \end{array}} \right) z^{m}(1-z)^{M-m}} \right] \) and finally \([1-(1-z)^{M}](Mz)^{-1}\).

  4. Quasi-null option prices imply that the payoff from salvaging wealth at the market price equals the proportional fair share. This result is consistent with the results of Plummer [26], who shows that if a project attainment fails to change the probability of supply of the public good (and thus remains uncertain), option price is zero.

  5. Ostroy [25] and Makowski [20] have characterized the economy equilibrium, such as the Edgeworth box, in terms of no-surplus condition. By the no-surplus condition, there is a price at which all trades must occur [13]. Nevertheless, the random-matching economies of traders that satisfy this condition are considered as pathological [11].

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Acknowledgments

This work was supported by the French National Research Agency through the Laboratory of Excellence ARBRE, a part of the Investments for the Future Program (ANR 11 – LABX-0002-01). It was also supported by the French National Forestry Office through the Forests for Tomorrow International Teaching and Research Chair. We are grateful to the associate editor and the anonymous referee for their thorough comments and suggestions, which significantly contributed to improving the quality of the paper.

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Authors and Affiliations

  1. Laboratoire d’Économie Forestière, Agro ParisTech, 54042, Nancy Cedex, France

    Arnaud Z. Dragicevic

  2. Laboratoire d’Économie Forestière, UMR 356, INRA, 54000, Nancy Cedex, France

    Arnaud Z. Dragicevic

  3. Chaire Forêts pour Demain, Agro ParisTech–Office National des Forêts, 54042, Nancy Cedex, France

    Arnaud Z. Dragicevic

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  1. Arnaud Z. Dragicevic
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Correspondence to Arnaud Z. Dragicevic.

Appendix

Appendix

See Tables 3, 4 and 5.

Table 3 Simulations of static option prices \(p\theta \), given p and k, for \(w=10\): \(p\theta =pw-gk^{-1}\)
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Table 4 Simulations of dynamic option prices \(p\theta \), given p and k, for \(w=10\): \(p\theta =pwM^{-1}-gk^{-1}[p(1-M)M^{-1}+1]\)
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Table 5 Simulations of dynamic option prices \(p\theta \), given z and k, for \(w=10\) and \(p=0.5\): \(p\theta =zgk^{-1}\)
Full size table

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Dragicevic, A.Z. Option Fund Market Dynamics for Threshold Public Goods. Dyn Games Appl 7, 21–33 (2017). https://doi.org/10.1007/s13235-015-0172-0

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