### Abstract

The estate division problem considers the issue of dividing an estate when the sum of entitlements is larger than the estate. This paper studies the estate division problem from a noncooperative perspective. The integer claim game introduced by O''Neill (1982) and extended by Atlamaz et al. (2011) is generalized by specifying a sharing rule to divide every interval among the claimants. We show that for all problems for which the sum of entitlements is at most twice the estate the existence of a Nash equilibrium is guaranteed for a general class of sharing rules. Moreover, the corresponding set of equilibrium payoffs is independent of which sharing rule in the class is used. Well-known division rules that always assign a payoff vector in this set of equilibrium payoffs are the adjusted proportional rule, the random arrival rule and the Talmud rule.

Original language | English |
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Pages (from-to) | 105-115 |

Number of pages | 11 |

Journal | Games and Economic Behavior |

Volume | 116 |

DOIs | |

Publication status | Published - Jul 2019 |

### Keywords

- Claim games
- Estate division problem
- Bankruptcy problem
- Adjusted proportional rule
- Random arrival rule
- Talmud rule
- THEORETIC ANALYSIS
- TAXATION PROBLEMS
- BANKRUPTCY
- PLAY

## Cite this

Peters, H., Schroeder, M., & Vermeulen, D. (2019). Claim games for estate division problems.

*Games and Economic Behavior*,*116*, 105-115. https://doi.org/10.1016/j.geb.2018.11.002