  One of the Multi-Agent Systems that is widely used by various government
agencies, buyers and sellers in a market economy, in such a manner so as to
attain optimized resource allocation, is the Combinatorial Auctioning System
(CAS). We study another important aspect of resource allocations in CAS, namely
fairness. We present two important notions of fairness in CAS, extended
fairness and basic fairness. We give an algorithm that works by incorporating a
metric to ensure fairness in a CAS that uses the Vickrey-Clark-Groves (VCG)
mechanism, and uses an algorithm of Sandholm to achieve optimality.
Mathematical formulations are given to represent measures of extended fairness
and basic fairness.
