### Abstract

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.

Original language | English (US) |
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Pages (from-to) | 135-164 |

Number of pages | 30 |

Journal | Games and Economic Behavior |

Volume | 98 |

DOIs | |

State | Published - Jul 1 2016 |

### Keywords

- Common-pool resource
- Inefficiency of equilibria
- Loss aversion
- Prospect theory
- Resource dilemma
- Risk heterogeneity
- Tragedy of the commons

### ASJC Scopus subject areas

- Finance
- Economics and Econometrics

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## Cite this

*Games and Economic Behavior*,

*98*, 135-164. https://doi.org/10.1016/j.geb.2016.06.003