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Sharing and growth in general random multiplicative environments

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  • Liebmann, Thomas
  • Kassberger, Stefan
  • Hellmich, Martin

Abstract

We extend the discrete-time cooperation evolution model proposed by Yaari and Solomon (2010) to a version with independent multiplicative random increments of arbitrary distribution and we develop a model in continuous time driven by exponential Lévy processes. In all settings, we prove that members of a sharing group enjoy a higher growth rate of their wealth and at the same time drastically reduce their exposure to random fluctuations: as more members join the group, the wealth of each member uniformly converges to a deterministic process growing at the highest possible rate. Thus, joining a sufficiently large sharing group may promise all its members to succeed almost surely even in environments where non-sharing individuals cannot escape misery on their own.

Suggested Citation

  • Liebmann, Thomas & Kassberger, Stefan & Hellmich, Martin, 2017. "Sharing and growth in general random multiplicative environments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 193-206.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:193-206
    DOI: 10.1016/j.ejor.2016.05.042
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