### Abstract

Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers’ incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable.

Original language | English |
---|---|

Pages (from-to) | 238-247 |

Number of pages | 10 |

Journal | Journal of Theoretical Biology |

Volume | 435 |

DOIs | |

Publication status | Published - 2017 Dec 21 |

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### Keywords

- Asymmetry
- Cooperation
- Nash equilibrium
- Public goods

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*435*, 238-247. https://doi.org/10.1016/j.jtbi.2017.09.006

**Asymmetric public goods game cooperation through pest control.** / Reeves, T.; Ohtsuki, H.; Fukui, Shin.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 435, pp. 238-247. https://doi.org/10.1016/j.jtbi.2017.09.006

}

TY - JOUR

T1 - Asymmetric public goods game cooperation through pest control

AU - Reeves, T.

AU - Ohtsuki, H.

AU - Fukui, Shin

PY - 2017/12/21

Y1 - 2017/12/21

N2 - Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers’ incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable.

AB - Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers’ incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable.

KW - Asymmetry

KW - Cooperation

KW - Nash equilibrium

KW - Public goods

UR - http://www.scopus.com/inward/record.url?scp=85030154340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030154340&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2017.09.006

DO - 10.1016/j.jtbi.2017.09.006

M3 - Article

C2 - 28939346

AN - SCOPUS:85030154340

VL - 435

SP - 238

EP - 247

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -