The AUCTEQ.ltx Model

Auctioning Classes to Students - Equilibrium problem

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The concept of a broker who maximizes producer-consumer surplus can be applied to auctions. Linear Programming is useful if the auction is complicated by features that might be interpreted as bidders with demand curves. This example is based on a design by R.L. Graves for a course registration system used since 1981 at the University of Chicago, in which students bid on courses.

Suppose there are *N* types of objects to be solve (e.g., courses), and there are *M* bidders (students). Bidder *i* is willing to pay up to *b _{ij}*,

There are a variety of ways of holding the auction. Let us suppose that it is a sealed-bid auction and we want to find a single, market-clearing price,

It is easy to determine the equilibrium

- at most,
Sunits of object_{j}jare sold;- any bid for
jless thanpdoes not buy a unit;_{j}p= 0 if less than_{j}Sunits of_{j}jare sold;- any bid for
jgreater thanpdoes buy a unit._{j}

In this example, we want to find a "market clearing" price for each object and an allocation of units to bidders so that each bidder is willing to accept the units awarded to him at the market clearing price. A bidder is satisfied with a particular unit if he cannot find another unit with a bigger difference between his maximum offer price and the market clearing price. This is equivalent to saying that each bidder maximizes his consumer surplus.

Keywords:

Marketing | Academia | Auctions | Demand Backlog | Dual Prices | Economic | Equilibrium |