Talmud: Talmud rule In ClaimsProblems: Analysis of Conflicting Claims

Description

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

Usage

 `1` ```Talmud(E, d, name = FALSE) ```

Arguments

 `E` The endowment. `d` The vector of claims. `name` A logical value.

Details

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) = CEL(E,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.

Value

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

References

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.

 ```1 2 3 4 5 6``` ```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) ```