Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competitive Equilibrium Relaxations in General Auctions   The goal of an auction is to determine commodity prices such that all
participants are perfectly happy. Such a solution is called a competitive
equilibrium and does not exist in general. For this reason we are interested in
solutions which are similar to a competitive equilibrium. The article
introduces two relaxations of a competitive equilibrium for general auctions.
Both relaxations determine one price per commodity by solving a difficult
non-convex optimization problem. The first model is a mathematical program with
equilibrium constraints (MPEC), which ensures that each participant is either
perfectly happy or his bid is rejected. An exact algorithm and a heuristic are
provided for this model. The second model is a relaxation of the first one and
only ensures that no participant incurs a loss. In an optimal solution to the
second model, no participant can be made better off without making another one
worse off.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat