An Introduction to Allocation Rules by Jens Leth Hougaard

By Jens Leth Hougaard

This booklet makes a speciality of studying price and surplus sharing difficulties in a scientific type. It bargains an in-depth research of varied varieties of principles for allocating a typical financial worth (cost) among individuals of a bunch or community – e.g. participants, agencies or items. the implications can assist readers overview the professionals and cons of many of the equipment considering phrases of assorted components resembling equity, consistency, balance, monotonicity and manipulability. As such, the publication represents an updated survey of expense and surplus sharing equipment for researchers, scholars and practitioners alike. The textual content is followed via sensible situations and various examples to make the theoretical effects simply accessible.

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Extra resources for An Introduction to Allocation Rules

Example text

N, ϕi (q, E) = 1 qi E − [nqi − Q]g(Q, E), Q Q where g : R2 → R is a continuous function. Since we require that a rationing rule must satisfy 0 ≤ ϕi (q, E) ≤ qi for all i, we have that g(Q, E) = 0. Note that the equal split rule (which is not a rationing rule as defined above since E/n may exceed qi for some i), satisfies No Advantageous Reallocation (g(Q, E) = E/n) but is manipulable by splitting. Likewise, equal split of the loss (that may result in negative shares) satisfies No Advantageous Reallocation (g(Q, E) = (E − Q)/n) but is manipulable by merging.

2) x1 + . . + xn = y1 + . . + yn . 2 Rationing Problems 23 and Olkin (1979). In terms of economics, x LD y can be interpreted as x being more equally distributed than y (less spread out). Now, it turns out that the constrained equal gains rule ϕCEG is the unique Lorenz-maximising rationing rule and dually, that the constraint equal loss rule ϕCEL is the unique Lorenz-minimising rationing rule. In other words, there is no other rule that results in more equally distributed shares than the constraint equal gains rule and no other rule that results in less equally distributed shares than the constraint equal loss rule.

In general, there are n! possible orderings of n agents. For each such ordering let agents receive as much of their demand as possible, that is if E > q1 then x1 = q1 and if E − x1 > q2 then x2 = q2 , etc. Now, the random priority rule assigns shares which are then defined as the average over all such orderings for each agent. In general, concerning models of priority, each agent is described not only by their demand (or claim), but by a combination of their demand and type. Another well known type is “time of arrival” – here a rule could be the familiar “first to arrive on the spot is the first to be served” rule which clearly violates order-preservation in terms of demand.

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