Summary UP
1.
UP is practivanle for dividing items 2 plaers begin by ranking the
items from best to worst
2.
Starting from top choice work down the list, naming independently 1
at a time the items they most prefer of those that remain. At each
stage, if A and B differ on their most
6. In either event both players get at least 50% unless A and B consider exactly
the same bundles to be minimal ( recall the comparison of UP with the ultimatum
game supplemented by a rule that allows B to make a counterproposal that will
be implementedshowing that this modified game in the qeuilibrium would be 50
cent 50 cents for one dollare.
11. id there are synergies, the an envy free split may be enhanced by the
sequential nature of UP which allows the player to choose items that complement
thoseuncontested items that they previously obtaine ( let us say ½ of a matching
sofa set you may then change your later preferences)
14. Compared to disputes over divisible items like money or Land dispute
The undercut procedure
Proposing a fair division procedure of Indivisible items between two players
Wherein each player ranks the items from best to worst
:
1) it is envy free
2) it may not be pareto optimal
Ency free split is always possible as long as the players differ on a minimal
bundle of items. A minimal bundle for a player is a subset that is worth at least
50% but, if reduced in any way ( in an ordinal sense), would be worth less than
50%.
The most difficult case : Players rank a set of items EXACTLY THE SAME> FOR
EXAMPLE SUPPOSE THERE ARE
1)
FIVE ITEMS RANKED 12345 FOR A and B
2)
A proposes that he takes 12 and b takes 345 ( the complimentary
subset . B can accept or reject
3)
If B undercuts, B it reduces A’s subset, B it reduces A’s subset to
one it values slightly less ( ie.g. 13) and giver the compliment 245
to A
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 Spring '11
 stevenjbrams
 Game Theory, 50%, 50 percent, 50 %, ITF

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