Talmud | R Documentation |

This function returns the awards vector assigned by the Talmud rule to a claims problem.

Talmud(E, d, name = FALSE)

`E` |
The endowment. |

`d` |
The vector of claims. |

`name` |
A logical value. |

Let *E≥ 0* be the endowment to be divided and *d* the vector of claims
with *d≥ 0* and such that *D=∑ di ≥ E*, the sum of claims *D* exceeds the endowment.

The Talmud rule coincides with the constrained equal awards rule (CEA)
applied to the problem *(E, d/2)* if the endowment is less or equal than the half-sum of the claims, *D/2*.
Otherwise, the Talmud rule assigns *d/2* and
the remainder, *E-D/2*, is awarded with the constrained equal losses rule with claims *d/2*. Therefore:

If *E≤ D/2* then:

*Talmud(E,d)=CEA(E,d/2).*

If *E≥ D/2* then:

*Talmud(E,d) =d/2+ CEL(E-D/2,d/2) = d-CEA(D-E,d/2).*

The Talmud rule when applied to a two-claimant problem is often referred to as the contested garment rule and coincides with concede-and-divide rule. The Talmud rule corresponds to the nucleolus of the associated (pessimistic) coalitional game.

The awards vector selected by the Talmud rule. If name = TRUE, the name of the function (Talmud) as a character string.

Aumann, R. and Maschler, M. (1985). Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36, 195-213.

Thomson, W. (2019). How to divide when there isn't enough. From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation. Cambridge University Press.

allrules, CEA, CEL, AA, APRO, RA, CD.

E=10 d=c(2,4,7,8) Talmud(E,d) D=sum(d) #The Talmud rule is self-dual d-Talmud(D-E,d)

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