Skip to main content
Log in

On the convergence of the random arrival rule in large claims problems

  • Original Paper
  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

We study the behavior of the random arrival rule in claims problems with a large number of claimants. We assume that the amount to divide is not too “small” compared with total claims, and each claim is not too “large” compared with any other positive claims. Then, the random arrival rule behaves like the proportional rule as the number of claimants increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213

    Article  Google Scholar 

  • Chun Y (1988) The proportional solution for rights problems. Math Soc Sci 15:231–246

    Article  Google Scholar 

  • Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520

    Article  Google Scholar 

  • Chun Y, Thomson W (2005) Convergence under replication of rules to adjudicate conflicting claims. Games Econ Behav 50:129–142

    Article  Google Scholar 

  • Debreu G, Scarf H (1963) A limit theorem on the core of an economy. Int Econ Rev 4:235–246

    Article  Google Scholar 

  • Moulin H (1987) Equal or proportional division of a surplus and other methods. Int J Game Theory 16: 161–186

    Article  Google Scholar 

  • O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371

    Article  Google Scholar 

  • Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II, annals of mathematics studies no 28. Princeton University Press, Princeton, NJ, pp 307–317

    Google Scholar 

  • Thomson W (1988) A study of choice correspondences in economies with a variable number of agents. J Econ Theory 46:237–254

    Article  Google Scholar 

  • Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45:249–297

    Article  Google Scholar 

  • Young HP (1987) On dividing an amount according to individual claims or liabilities. Math Oper Res 12:398–414

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Youngsub Chun.

Additional information

We are grateful to Yuki Funaki, William Thomson, and three referees for their comments. This work was supported by the Brain Korea 21 Project in 2003

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chun, Y., Lee, J. On the convergence of the random arrival rule in large claims problems. Int J Game Theory 36, 259–273 (2007). https://doi.org/10.1007/s00182-007-0075-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00182-007-0075-4

Keywords

JEL Classification Numbers

Navigation