We consider reallocation problems in settings where the initial endowment of
each agent consists of a subset of the resources. The private information of
the players is their value for every possible subset of the resources. The goal
is to redistribute resources among agents to maximize efficiency. Monetary
transfers are allowed, but participation is voluntary.
We develop incentive-compatible, individually-rational and budget balanced
mechanisms for several classic settings, including bilateral trade, partnership
dissolving, Arrow-Debreu markets, and combinatorial exchanges. All our
mechanisms (except one) provide a constant approximation to the optimal
efficiency in these settings, even in ones where the preferences of the agents
are complex multi-parameter functions
