Journal of Mathematical Biology

, Volume 72, Issue 4, pp 997–1010 | Cite as

Evolutionary dynamics of collective index insurance

  • Jorge M. Pacheco
  • Francisco C. Santos
  • Simon A. LevinEmail author


Index-based insurances offer promising opportunities for climate-risk investments in developing countries. Indeed, contracts conditional on, e.g., weather or livestock indexes can be cheaper to set up than conventional indemnity-based insurances, while offering a safety net to vulnerable households, allowing them to eventually escape poverty traps. Moreover, transaction costs by insurance companies may be additionally reduced if contracts, instead of arranged with single households, are endorsed by collectives of households that bear the responsibility of managing the division of the insurance coverage by its members whenever the index is surpassed, allowing for additional flexibility in what concerns risk-sharing and also allowing insurance companies to avoid the costs associated with moral hazard. Here we resort to a population dynamics framework to investigate under which conditions household collectives may find collective index insurances attractive, when compared with individual index insurances. We assume risk sharing among the participants of each collective, and model collective action in terms of an N-person threshold game. Compared to less affordable individual index insurances, we show how collective index insurances lead to a coordination problem in which the adoption of index insurances may become the optimal decision, spreading index insurance coverage to the entire population. We further investigate the role of risk-averse and risk-prone behaviors, as well as the role of partial correlation between insurance coverage and actual loss of crops, and in which way these affect the original coordination thresholds.


Index insurance Collective action Evolutionary game theory Non-linear returns 

Mathematics Subject Classification

91-XX 91A22 91A06 91A40 91B18 91B30 



The authors would like to dedicate this paper to Mats Gyllenberg on the occasion of his 60th birthday. We also thank Avinash Dixit for his insightful comments. J.M.P. and F.C.S. acknowledge financial support from FCT-Portugal through Grants EXPL/EEI-SII/2556/2013, PTDC/MAT-STA/3358/2014, and PTDC/EEI-SII/5081/2014, and by multi-annual funding of CBMA-UM and INESC-ID (under the Projects UID/BIA/04050/2013 and UID/CEC/50021/2013) provided by FCT-Portugal. S.A.L. acknowledges financial support from National Science Foundation Grants EF-1137894, GEO-1211972 and Project “Green Growth Based on Marine Resources: Ecological and Socio-Economic Constraints (GreenMAR)”, funded by Nordforsk.

Compliance with ethical standards

Conflict of interest

The authors declare no competing financial interests.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Centro de Biologia Molecular e AmbientalUniversidade do MinhoBragaPortugal
  2. 2.Departamento de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal
  3. 3.ATP-GroupLisbon CodexPortugal
  4. 4.INESC-ID and Instituto Superior TécnicoUniversidade de Lisboa, IST-TagusparquePorto SalvoPortugal
  5. 5.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA
  6. 6.Resources for the FutureUniversity FellowWashingtonUSA
  7. 7.Beijer Institute of Ecological EconomicsStockholmSweden

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