When designing a mechanism there are several desirable properties to
maintain such as incentive compatibility (IC), individual
rationality (IR), and budget balance (BB). It is well known
\cite{MS83} that it is impossible for a mechanism to maximize social
welfare whilst also being IR, IC, and BB. There have been several
attempts to circumvent \cite{MS83} by trading welfare for BB, e.g.,
in domains such as double-sided auctions\cite{Mcafee91}, distributed
markets\cite{BNP04} and supply chain
problems\cite{Bab01,Bab03}.
In this paper we provide a procedure called a Generalized Trade Reduction
(GTR) for single-value players, which given an IR and IC mechanism,
outputs a mechanism that is IR, IC and BB with a loss of welfare. We bound the
welfare achieved by our procedure for a wide range of domains. In particular,
our results improve on existing solutions for problems such as double-sided
markets with homogenous goods, distributed markets and several kinds of supply
chains. Furthermore, our solution provides budget balanced mechanisms for
several open problems such as combinatorial double-sided auctions and
distributed markets with strategic transportation edges.