expectation senses. A significant reduction in efficiency loss is obtained for both linear
rebate mechanisms when compared to the VCG mechanism. Also, as number of agents
increases the efficiency loss tends to zero for the proposed mechanisms in the respective
We also discussed extensions of our proposed mechanisms to a case where the valu-
ation functions are private information to agents. The agents report only scalar values
and surrogate valuation functions are constructed from them (Johari & Tsitsiklis in ).
A similar optimization will yield almost budget balanced and efficient Nash equilibrium
implementation for this setting. Mechanisms outside Groves class that are more com-
petitive but inefficient were proposed in . Issues related to their extensions to the
divisible case were also discussed. Issues while implementing mechanisms without money
were also discussed for different possible valuation functions.
In this work, we restricted ourselves to linear redistribution mechanisms. We believe
that there can be nonlinear redistribution mechanisms which are more budget balanced
than linear ones for divisible resource allocation. Therefore, investigating possible nonlin-
ear redistribution mechanisms will be an interesting future direction. Another possible
extension is to look for more budget balanced but allocatively inefficient and/or non
strategy proof mechanisms. The design of mechanisms without money that achieve
lower efficiency loss is also a possible area of future research.