### 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) |
---|---|

Pages (from-to) | 135-164 |

Number of pages | 30 |

Journal | Games and Economic Behavior |

Volume | 98 |

DOIs | |

State | Published - Jul 1 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Economics and Econometrics
- Finance

### Cite this

*Games and Economic Behavior*,

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

**Fragility of the commons under prospect-theoretic risk attitudes.** / Hota, Ashish R.; Garg, Siddharth; Sundaram, Shreyas.

Research output: Contribution to journal › Article

*Games and Economic Behavior*, vol. 98, pp. 135-164. https://doi.org/10.1016/j.geb.2016.06.003

}

TY - JOUR

T1 - Fragility of the commons under prospect-theoretic risk attitudes

AU - Hota, Ashish R.

AU - Garg, Siddharth

AU - Sundaram, Shreyas

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

KW - Common-pool resource

KW - Inefficiency of equilibria

KW - Loss aversion

KW - Prospect theory

KW - Resource dilemma

KW - Risk heterogeneity

KW - Tragedy of the commons

UR - http://www.scopus.com/inward/record.url?scp=84976619721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976619721&partnerID=8YFLogxK

U2 - 10.1016/j.geb.2016.06.003

DO - 10.1016/j.geb.2016.06.003

M3 - Article

VL - 98

SP - 135

EP - 164

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

ER -