This function returns the awards vector assigned by the Talmud rule to a claims problem.
The vector of claims.
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:
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.
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.
1 2 3 4 5 6
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.